{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "02000000",
   "metadata": {},
   "source": [
    "# Rachunek prawdopodobieństwa i zmienne losowe\n",
    "\n",
    "Prawdopodobieństwo jest językiem niepewności: pozwala formalnie opisywać losowość i zmienność.\n",
    "\n",
    "W tym kursie trzymamy się przede wszystkim **interpretacji częstotliwościowej**: prawdopodobieństwo zdarzenia rozumiemy jako graniczną częstość w bardzo długiej serii powtórzeń (przy stałych warunkach)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000001",
   "metadata": {},
   "source": [
    "## Cele\n",
    "\n",
    "Po tym wykładzie:\n",
    "\n",
    "- Rozumiesz, jak w podejściu **częstotliwościowym** interpretować prawdopodobieństwo (jako częstość w długim okresie).\n",
    "- Umiesz pracować z pojęciami: przestrzeń zdarzeń, zdarzenie, suma/przecięcie, dopełnienie, prawdopodobieństwo warunkowe.\n",
    "- Umiesz policzyć proste prawdopodobieństwa „dokładnie” (enumeracja) oraz przez symulację.\n",
    "- Rozumiesz różnicę między zmienną losową dyskretną i ciągłą.\n",
    "- Potrafisz obliczyć (na prostym przykładzie) wartość oczekiwaną i wariancję zmiennej losowej dyskretnej.\n",
    "- Umiesz zastosować twierdzenie Bayesa na prostym przykładzie oraz interpretować wynik w kategoriach naturalnych częstości."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "02000003",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from scipy import stats\n",
    "\n",
    "from IPython.display import display\n",
    "\n",
    "SEED = 20250116\n",
    "\n",
    "sns.set_theme(style='whitegrid')\n",
    "\n",
    "try:\n",
    "    import ipywidgets as widgets\n",
    "\n",
    "    WIDGETY_DOSTEPNE = True\n",
    "except ImportError:\n",
    "    widgets = None\n",
    "    WIDGETY_DOSTEPNE = False"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000004",
   "metadata": {},
   "source": [
    "## Prawdopodobieństwo: intuicja częstotliwościowa\n",
    "\n",
    "Prawdopodobieństwo bywa trochę zdradliwe. Każdy używa tego słowa w codziennym języku, ale kiedy przechodzimy do analizy danych, okazuje się, że potrzebujemy znaczenia precyzyjnego i operacyjnego.\n",
    "\n",
    "W tym notatniku przyjmujemy punkt wyjścia klasycznej statystyki: $P(A)$ interpretujemy jako **częstość względną zdarzenia $A$ w bardzo długiej serii powtórzeń** tego samego doświadczenia, prowadzonych w tych samych warunkach. To ważne, bo później dokładnie to założenie stoi za rozumieniem rozkładów, błędów losowych i testów."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcfc76fb",
   "metadata": {},
   "source": [
    "### Trzy sposoby mówienia o prawdopodobieństwie\n",
    "\n",
    "W literaturze spotyka się co najmniej trzy sensowne sposoby rozumienia prawdopodobieństwa i dobrze je rozróżniać, bo każdy odpowiada na trochę inne pytanie.\n",
    "\n",
    "Pierwszy to język **analityczny**: jeśli umiemy wypisać wszystkie równoprawdopodobne możliwości, to prawdopodobieństwo liczymy jako udział przypadków „sprzyjających” w całości. Tak działają klasyczne zadania z kostkami i kartami.\n",
    "\n",
    "Drugi to język **częstotliwościowy**: nie pytamy, ile jest możliwości na papierze, tylko co dzieje się w długiej serii rzeczywistych powtórzeń. Ten sposób myślenia jest osią całego kursu, bo najbliżej łączy się z tym, jak faktycznie pracujemy na danych empirycznych.\n",
    "\n",
    "Trzeci to język **subiektywny**: prawdopodobieństwo opisuje stopień przekonania, który aktualizujemy wraz z nową informacją. Ten punkt widzenia pojawi się u nas przy twierdzeniu Bayesa.\n",
    "\n",
    "Ta trzy rozumienia nie muszą się wykluczać. W praktyce badawczej często przełączamy się między nimi, ale warto wiedzieć, kiedy dokładnie zmieniamy znaczenie słowa „prawdopodobieństwo”."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000005",
   "metadata": {},
   "source": [
    "### Wymuszony wybór w kognitywistyce (2AFC)\n",
    "\n",
    "Na krótkim odcinku częstości zwykle \"pływają\" i potrafią wyglądać myląco. Dopiero kiedy liczba prób rośnie, zaczynamy widzieć stabilizację.\n",
    "\n",
    "Zaczniemy od przykładu z kognitywistyki: zadania dwuwyborowego, w którym każda próba kończy się odpowiedzią poprawną albo błędną.\n",
    "\n",
    "W zadaniu typu 2AFC w każdej próbie badany musi wybrać **jedną z dwóch** odpowiedzi.\n",
    "\n",
    "Przykład: w dwóch krótkich przedziałach czasowych odtwarzany jest dźwięk; dźwięk pojawia się w jednym z nich, a zadaniem jest wskazać, czy był w pierwszym czy w drugim.\n",
    "\n",
    "Jeżeli zapisujemy wynik tylko jako „poprawnie / błędnie”, to pojedyncza próba ma dwa możliwe wyniki (0/1). Taki model nazywamy **próbą Bernoulliego**. Jej parametrem jest $p$ — prawdopodobieństwo odpowiedzi poprawnej (przy stałych warunkach zadania).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "02000006",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.5       , 0.66666667, 0.5       , 0.4       ,\n",
       "       0.5       , 0.57142857, 0.5       , 0.55555556, 0.6       ])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = np.random.default_rng(SEED)\n",
    "\n",
    "p_poprawnej_odpowiedzi = 0.55\n",
    "liczba_prob = 500\n",
    "\n",
    "poprawna_odpowiedz = rng.random(liczba_prob) < p_poprawnej_odpowiedzi\n",
    "estymata_skumulowana = np.cumsum(poprawna_odpowiedz) / np.arange(1, liczba_prob + 1)\n",
    "\n",
    "estymata_skumulowana[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "02000007",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(estymata_skumulowana, linewidth=2)\n",
    "plt.axhline(p_poprawnej_odpowiedzi, linestyle='--', color='black', label='p (założone)')\n",
    "\n",
    "plt.title('Zadanie 2AFC: częstość skumulowana jako estymator p')\n",
    "plt.xlabel('Liczba prób')\n",
    "plt.ylabel('Częstość odpowiedzi poprawnych')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000008",
   "metadata": {},
   "source": [
    "### Widżet: jak szybko stabilizuje się częstość?\n",
    "\n",
    "Ustaw $p$ oraz liczbę prób i zobacz, jak zachowuje się częstość skumulowana w zadaniu dwuwyborowym."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "02000009",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "164d0ea742f64fa78cbb9fd9c1cce263",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(FloatSlider(value=0.7, description='p', max=0.95, min=0.05, step=0.01), IntSlider(value=2000, d…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8b74f1b6c9934ce2aed1b454290fca3d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if not WIDGETY_DOSTEPNE:\n",
    "    print('Widżety nie są dostępne: zainstaluj pakiet ipywidgets, aby korzystać z części interaktywnych.')\n",
    "else:\n",
    "    p_slider = widgets.FloatSlider(\n",
    "        value=0.7,\n",
    "        min=0.05,\n",
    "        max=0.95,\n",
    "        step=0.01,\n",
    "        description='p',\n",
    "        readout_format='.2f',\n",
    "    )\n",
    "    liczba_prob_slider = widgets.IntSlider(\n",
    "        value=2000,\n",
    "        min=100,\n",
    "        max=20000,\n",
    "        step=100,\n",
    "        description='Liczba prób',\n",
    "    )\n",
    "    seed_input = widgets.IntText(value=SEED, description='Ziarno')\n",
    "\n",
    "    def pokaz_stabilizacje(p, liczba_prob, seed):\n",
    "        rng = np.random.default_rng(seed)\n",
    "        poprawna_odpowiedz = rng.random(liczba_prob) < p\n",
    "        estymata_skumulowana = np.cumsum(poprawna_odpowiedz) / np.arange(1, liczba_prob + 1)\n",
    "\n",
    "        plt.figure(figsize=(10, 4))\n",
    "        plt.plot(estymata_skumulowana, linewidth=2)\n",
    "        plt.axhline(p, linestyle='--', color='black', label='p')\n",
    "\n",
    "        plt.title('Zadanie 2AFC: stabilizacja częstości skumulowanej')\n",
    "        plt.xlabel('Liczba prób')\n",
    "        plt.ylabel('Częstość odpowiedzi poprawnych')\n",
    "        plt.ylim(0.0, 1.0)\n",
    "        plt.legend()\n",
    "        plt.show()\n",
    "\n",
    "    out = widgets.interactive_output(\n",
    "        pokaz_stabilizacje,\n",
    "        {'p': p_slider, 'liczba_prob': liczba_prob_slider, 'seed': seed_input},\n",
    "    )\n",
    "\n",
    "    display(widgets.VBox([p_slider, liczba_prob_slider, seed_input]), out)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000010",
   "metadata": {},
   "source": [
    "### Uwaga: „te same warunki” w eksperymencie to założenie\n",
    "\n",
    "Interpretacja częstotliwościowa mówi o powtarzaniu doświadczenia w identycznych warunkach. W prawdziwym eksperymencie bywa inaczej: badany może się uczyć, męczyć albo zmieniać strategię. Wtedy prawdopodobieństwo odpowiedzi poprawnej może się **zmieniać w czasie**.\n",
    "\n",
    "Poniżej prosta symulacja, w której $p$ rośnie liniowo (uczenie). Zobacz, jak to wpływa na częstość skumulowaną."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "02000011",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.default_rng(SEED + 10)\n",
    "\n",
    "liczba_prob = 2000\n",
    "p_poczatek = 0.55\n",
    "p_koniec = 0.80\n",
    "\n",
    "p_w_czasie = np.linspace(p_poczatek, p_koniec, liczba_prob)\n",
    "\n",
    "poprawna_odpowiedz = rng.random(liczba_prob) < p_w_czasie\n",
    "estymata_skumulowana = np.cumsum(poprawna_odpowiedz) / np.arange(1, liczba_prob + 1)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(estymata_skumulowana, linewidth=2, label='częstość skumulowana')\n",
    "plt.plot(p_w_czasie, linestyle='--', color='black', alpha=0.7, label='p w czasie (uczenie)')\n",
    "\n",
    "plt.title('Gdy warunki nie są stałe: p zmienia się w czasie')\n",
    "plt.xlabel('Liczba prób')\n",
    "plt.ylabel('Częstość odpowiedzi poprawnych')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000012",
   "metadata": {},
   "source": [
    "## Zdarzenia i podstawowe reguły\n",
    "\n",
    "Zaczynamy od słownika, którym posługuje się rachunek prawdopodobieństwa.\n",
    "\n",
    "- **Przestrzeń zdarzeń elementarnych** $\\Omega$ to zbiór wszystkich możliwych wyników doświadczenia.\n",
    "- **Zdarzenie** $A$ to podzbiór $\\Omega$ (czyli: pewna grupa wyników, które nas interesują).\n",
    "\n",
    "Jeżeli wszystkie wyniki elementarne są jednakowo prawdopodobne (np. uczciwa kostka), to:\n",
    "\n",
    "$$\n",
    "P(A) = \\frac{|A|}{|\\Omega|}\n",
    "$$\n",
    "\n",
    "Najczęściej używane operacje na zdarzeniach:\n",
    "\n",
    "- **dopełnienie** $A^c$ („nie A”),\n",
    "- **suma** $A\\cup B$ („A lub B”),\n",
    "- **przecięcie** $A\\cap B$ („A i B”).\n",
    "\n",
    "Przydają nam się też dwa wzory:\n",
    "\n",
    "- reguła dodawania: $P(A\\cup B)=P(A)+P(B)-P(A\\cap B)$,\n",
    "- prawdopodobieństwo warunkowe: $P(A\\mid B)=\\frac{P(A\\cap B)}{P(B)}$ (dla $P(B)>0$).\n",
    "\n",
    "Zobaczmy to na przykładzie dwóch rzutów uczciwą kostką. Zrobimy to „dokładnie” przez enumerację (wypisanie całej $\\Omega$).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "02000013",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Liczba wyników w Ω: 36\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>d1</th>\n",
       "      <th>d2</th>\n",
       "      <th>suma</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   d1  d2  suma\n",
       "0   1   1     2\n",
       "1   1   2     3\n",
       "2   1   3     4\n",
       "3   1   4     5\n",
       "4   1   5     6\n",
       "5   1   6     7\n",
       "6   2   1     3\n",
       "7   2   2     4\n",
       "8   2   3     5\n",
       "9   2   4     6"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "outcomes = []\n",
    "\n",
    "for d1 in range(1, 7):\n",
    "    for d2 in range(1, 7):\n",
    "        outcomes.append({'d1': d1, 'd2': d2})\n",
    "\n",
    "omega_df = pd.DataFrame(outcomes)\n",
    "omega_df['suma'] = omega_df['d1'] + omega_df['d2']\n",
    "\n",
    "def prob(mask):\n",
    "    return mask.mean()\n",
    "\n",
    "print('Liczba wyników w Ω:', int(omega_df.shape[0]))\n",
    "omega_df.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "02000014",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(A) (enumeracja) = 0.16666666666666666\n",
      "P(B) (enumeracja) = 0.3055555555555556\n",
      "P(A) (symulacja Monte Carlo) = 0.16763\n",
      "P(B) (symulacja Monte Carlo) = 0.305095\n"
     ]
    }
   ],
   "source": [
    "# A: suma oczek = 7\n",
    "A = omega_df['suma'] == 7\n",
    "\n",
    "# B: przynajmniej jedna szóstka\n",
    "B = (omega_df['d1'] == 6) | (omega_df['d2'] == 6)\n",
    "\n",
    "p_A = prob(A)\n",
    "p_B = prob(B)\n",
    "\n",
    "print('P(A) (enumeracja) =', p_A)\n",
    "print('P(B) (enumeracja) =', p_B)\n",
    "\n",
    "# Symulacja jako kontrola intuicji\n",
    "rng = np.random.default_rng(SEED + 1)\n",
    "n_sim = 200_000\n",
    "\n",
    "d1_sim = rng.integers(1, 7, size=n_sim)\n",
    "d2_sim = rng.integers(1, 7, size=n_sim)\n",
    "\n",
    "p_A_mc = np.mean(d1_sim + d2_sim == 7)\n",
    "p_B_mc = np.mean((d1_sim == 6) | (d2_sim == 6))\n",
    "\n",
    "print('P(A) (symulacja Monte Carlo) =', p_A_mc)\n",
    "print('P(B) (symulacja Monte Carlo) =', p_B_mc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "02000015",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(A ∪ B) = 0.4166666666666667\n",
      "P(A)+P(B)-P(A ∩ B) = 0.41666666666666663\n"
     ]
    }
   ],
   "source": [
    "p_union = prob(A | B)\n",
    "p_intersection = prob(A & B)\n",
    "\n",
    "# Reguła dodawania:\n",
    "# P(A \\cup B) = P(A) + P(B) - P(A \\cap B)\n",
    "p_union_rhs = p_A + p_B - p_intersection\n",
    "\n",
    "print('P(A ∪ B) =', p_union)\n",
    "print('P(A)+P(B)-P(A ∩ B) =', p_union_rhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "02000016",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(C) = 0.16666666666666666\n",
      "P(A ∩ C) = 0.027777777777777776\n",
      "P(A | C) = 0.16666666666666666\n",
      "P(A | C) (w podzbiorze) = 0.16666666666666666\n"
     ]
    }
   ],
   "source": [
    "# Prawdopodobieństwo warunkowe: P(A | C) = P(A \\cap C) / P(C)\n",
    "# C: pierwszy rzut to 3\n",
    "C = omega_df['d1'] == 3\n",
    "\n",
    "p_C = prob(C)\n",
    "p_A_and_C = prob(A & C)\n",
    "p_A_given_C = p_A_and_C / p_C\n",
    "\n",
    "# To samo można policzyć jako \"odsetek A\" w podzbiorze spełniającym C\n",
    "p_A_given_C_alt = (omega_df.loc[C, 'suma'] == 7).mean()\n",
    "\n",
    "print('P(C) =', p_C)\n",
    "print('P(A ∩ C) =', p_A_and_C)\n",
    "print('P(A | C) =', p_A_given_C)\n",
    "print('P(A | C) (w podzbiorze) =', p_A_given_C_alt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000017",
   "metadata": {},
   "source": [
    "### Zdarzenia w danych eksperymentalnych: poprawność i czas reakcji\n",
    "\n",
    "W praktyce zdarzenia często definiuje się na danych: np. „odpowiedź była poprawna” albo „czas reakcji był krótszy niż 450 ms”.\n",
    "\n",
    "Poniżej tworzymy mały, sztuczny zbiór danych z prób zadania z wymuszonym wyborem i liczymy kilka prawdopodobieństw tak samo, jak przy kostkach (częstość = średnia wartości logicznych).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "02000018",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(poprawna) = 0.67\n",
      "P(szybka) = 0.105\n",
      "P(poprawna ∩ szybka) = 0.1\n",
      "P(poprawna | szybka) = 0.9523809523809524\n",
      "P(poprawna | wolniejsza) = 0.6368715083798882\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>czas_reakcji_ms</th>\n",
       "      <th>poprawna</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>540.065260</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>633.963861</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>577.287164</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>546.199071</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>528.175305</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>641.879533</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>604.194082</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>543.255568</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>562.511407</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>657.449812</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   czas_reakcji_ms  poprawna\n",
       "0       540.065260      True\n",
       "1       633.963861      True\n",
       "2       577.287164     False\n",
       "3       546.199071      True\n",
       "4       528.175305      True\n",
       "5       641.879533      True\n",
       "6       604.194082      True\n",
       "7       543.255568     False\n",
       "8       562.511407     False\n",
       "9       657.449812     False"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = np.random.default_rng(SEED + 2)\n",
    "\n",
    "liczba_prob = 200\n",
    "\n",
    "czas_reakcji_ms = rng.normal(loc=550, scale=90, size=liczba_prob)\n",
    "czas_reakcji_ms = np.clip(czas_reakcji_ms, 200, None)\n",
    "\n",
    "proby_df = pd.DataFrame({'czas_reakcji_ms': czas_reakcji_ms})\n",
    "\n",
    "szybka = proby_df['czas_reakcji_ms'] < 450\n",
    "p_poprawna = np.where(szybka, 0.80, 0.65)\n",
    "\n",
    "proby_df['poprawna'] = rng.random(liczba_prob) < p_poprawna\n",
    "\n",
    "p_poprawna_all = prob(proby_df['poprawna'])\n",
    "p_szybka = prob(szybka)\n",
    "p_poprawna_i_szybka = prob(proby_df['poprawna'] & szybka)\n",
    "\n",
    "print('P(poprawna) =', p_poprawna_all)\n",
    "print('P(szybka) =', p_szybka)\n",
    "print('P(poprawna ∩ szybka) =', p_poprawna_i_szybka)\n",
    "print('P(poprawna | szybka) =', p_poprawna_i_szybka / p_szybka)\n",
    "print('P(poprawna | wolniejsza) =', prob(proby_df['poprawna'] & ~szybka) / prob(~szybka))\n",
    "\n",
    "proby_df.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a90329e",
   "metadata": {},
   "source": [
    "### Jedna tabela, trzy rodzaje prawdopodobieństwa\n",
    "\n",
    "W tym samym zbiorze danych możemy policzyć trzy różne rzeczy i każda odpowiada na inne pytanie.\n",
    "\n",
    "Prawdopodobieństwo **zwykłe** mówi, jak często zachodzi pojedyncza własność (np. poprawna odpowiedź). Prawdopodobieństwo **łączne** opisuje współwystępowanie dwóch własności jednocześnie (np. poprawna i szybka). Prawdopodobieństwo **warunkowe** zmienia perspektywę: interesuje nas poprawność, ale tylko wewnątrz wybranego podzbioru (np. tylko w próbach szybkich).\n",
    "\n",
    "To rozróżnienie wydaje się drobne, ale w praktyce jest kluczowe: wiele błędów interpretacyjnych bierze się z mieszania tych trzech poziomów."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "99170eb5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>szybka</th>\n",
       "      <th>False</th>\n",
       "      <th>True</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>poprawna</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>False</th>\n",
       "      <td>65</td>\n",
       "      <td>1</td>\n",
       "      <td>66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>114</td>\n",
       "      <td>20</td>\n",
       "      <td>134</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>179</td>\n",
       "      <td>21</td>\n",
       "      <td>200</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "szybka    False  True  All\n",
       "poprawna                  \n",
       "False        65     1   66\n",
       "True        114    20  134\n",
       "All         179    21  200"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(poprawna) = 0.67\n",
      "P(szybka) = 0.105\n",
      "P(poprawna ∩ szybka) = 0.1\n",
      "P(poprawna | szybka) = 0.9523809523809524\n",
      "\n",
      "Interpretacja:\n",
      "- P(poprawna) dotyczy całej próby.\n",
      "- P(poprawna ∩ szybka) dotyczy tylko prób spełniających oba warunki naraz.\n",
      "- P(poprawna | szybka) porównuje poprawność wewnątrz podzbioru prób szybkich.\n"
     ]
    }
   ],
   "source": [
    "tabela_2x2 = pd.crosstab(\n",
    "    proby_df['poprawna'],\n",
    "    szybka,\n",
    "    rownames=['poprawna'],\n",
    "    colnames=['szybka'],\n",
    "    margins=True,\n",
    ")\n",
    "\n",
    "display(tabela_2x2)\n",
    "\n",
    "p_poprawna = prob(proby_df['poprawna'])\n",
    "p_szybka = prob(szybka)\n",
    "p_poprawna_i_szybka = prob(proby_df['poprawna'] & szybka)\n",
    "p_poprawna_gdy_szybka = p_poprawna_i_szybka / p_szybka\n",
    "\n",
    "print('P(poprawna) =', p_poprawna)\n",
    "print('P(szybka) =', p_szybka)\n",
    "print('P(poprawna ∩ szybka) =', p_poprawna_i_szybka)\n",
    "print('P(poprawna | szybka) =', p_poprawna_gdy_szybka)\n",
    "\n",
    "print()\n",
    "print('Interpretacja:')\n",
    "print('- P(poprawna) dotyczy całej próby.')\n",
    "print('- P(poprawna ∩ szybka) dotyczy tylko prób spełniających oba warunki naraz.')\n",
    "print('- P(poprawna | szybka) porównuje poprawność wewnątrz podzbioru prób szybkich.')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000019",
   "metadata": {},
   "source": [
    "### Niezależność\n",
    "\n",
    "Intuicyjnie: zdarzenia $A$ i $B$ są niezależne, gdy informacja o jednym z nich **nie zmienia** prawdopodobieństwa drugiego.\n",
    "\n",
    "Formalnie (równoważne warunki):\n",
    "\n",
    "- $P(A \\cap B) = P(A)P(B)$,\n",
    "- albo $P(A\\mid B)=P(A)$ (dla $P(B)>0$).\n",
    "\n",
    "Sprawdźmy to na prostym przykładzie: parzystość pierwszego i drugiego rzutu kostką.\n",
    "\n",
    "Niech:\n",
    "\n",
    "- $E_1$ = „pierwszy rzut parzysty”,\n",
    "- $E_2$ = „drugi rzut parzysty”.\n",
    "\n",
    "Uwaga: w eksperymentach kolejne próby mogą nie być niezależne (np. uczenie, zmęczenie, efekt poprzedniego bodźca). Niezależność jest więc założeniem modelu, które warto świadomie oceniać.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "02000020",
   "metadata": {},
   "outputs": [],
   "source": [
    "E1 = omega_df['d1'] % 2 == 0\n",
    "E2 = omega_df['d2'] % 2 == 0\n",
    "\n",
    "p_E1 = prob(E1)\n",
    "p_E2 = prob(E2)\n",
    "p_E1_and_E2 = prob(E1 & E2)\n",
    "\n",
    "p_E1_given_E2 = p_E1_and_E2 / p_E2\n",
    "\n",
    "print('P(E1) =', p_E1)\n",
    "print('P(E2) =', p_E2)\n",
    "print('P(E1 ∩ E2) =', p_E1_and_E2)\n",
    "print('P(E1)P(E2) =', p_E1 * p_E2)\n",
    "print('P(E1 | E2) =', p_E1_given_E2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eee6c97a",
   "metadata": {},
   "source": [
    "### Zwracanie i niezależność: drobny szczegół, duża różnica\n",
    "\n",
    "Wzór $P(A \\cap B)=P(A)P(B)$ działa tylko wtedy, gdy zdarzenia są niezależne. Najprostszy sposób, by to poczuć, to porównać losowanie **ze zwracaniem** i **bez zwracania**.\n",
    "\n",
    "Przy zwracaniu skład populacji po każdej próbie wraca do punktu wyjścia, więc szanse kolejnych wyników są stałe. Bez zwracania pierwszy wynik zmienia warunki drugiego losowania. To właśnie ta zmiana łamie niezależność.\n",
    "\n",
    "W praktyce badań behawioralnych analogia jest bardzo użyteczna: jeżeli poprzednie próby zmieniają zachowanie uczestnika (uczenie, zmęczenie, adaptacja), to „losowania” kolejnych odpowiedzi też przestają być niezależne."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "a05b34b8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(niebieski, niebieski) ze zwracaniem (symulacja): 0.057433333333333336\n",
      "P(niebieski, niebieski) ze zwracaniem (teoria):    0.0576\n",
      "\n",
      "P(niebieski, niebieski) bez zwracania (symulacja): 0.05608\n",
      "P(niebieski, niebieski) bez zwracania (teoria):    0.055757575757575756\n"
     ]
    }
   ],
   "source": [
    "rng = np.random.default_rng(SEED + 30)\n",
    "\n",
    "n_sim = 300_000\n",
    "p_blue = 24 / 100\n",
    "\n",
    "# Ze zwracaniem: oba losowania mają to samo p = 24/100.\n",
    "pierwszy_zz = rng.random(n_sim) < p_blue\n",
    "drugi_zz = rng.random(n_sim) < p_blue\n",
    "p_bb_zz = np.mean(pierwszy_zz & drugi_zz)\n",
    "\n",
    "# Bez zwracania: p w drugim losowaniu zależy od wyniku pierwszego.\n",
    "pierwszy_bz = rng.random(n_sim) < p_blue\n",
    "p_drugi_bz = np.where(pierwszy_bz, 23 / 99, 24 / 99)\n",
    "drugi_bz = rng.random(n_sim) < p_drugi_bz\n",
    "p_bb_bz = np.mean(pierwszy_bz & drugi_bz)\n",
    "\n",
    "print('P(niebieski, niebieski) ze zwracaniem (symulacja):', p_bb_zz)\n",
    "print('P(niebieski, niebieski) ze zwracaniem (teoria):   ', p_blue * p_blue)\n",
    "\n",
    "print('\\nP(niebieski, niebieski) bez zwracania (symulacja):', p_bb_bz)\n",
    "print('P(niebieski, niebieski) bez zwracania (teoria):   ', (24 / 100) * (23 / 99))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000021",
   "metadata": {},
   "source": [
    "## Zmienne losowe: dyskretne i ciągłe\n",
    "\n",
    "W rachunku prawdopodobieństwa często nie analizujemy samego wyniku doświadczenia, lecz przypisujemy każdemu wynikowi liczbę opisującą interesującą nas cechę. Tę funkcję, która każdemu wynikowi przyporządkowuje liczbę, nazywamy **zmienną losową**.\n",
    "\n",
    "Przykłady:\n",
    "\n",
    "- $X$ = liczba odpowiedzi poprawnych w 10 próbach zadania dwuwyborowego (zmienna **dyskretna**),\n",
    "- $Y$ = czas reakcji w ms (zmienna **ciągła**),\n",
    "- $Z$ = średnica źrenicy w mm (zmienna **ciągła**).\n",
    "\n",
    "**Zmienna losowa dyskretna** przyjmuje wartości policzalne.\n",
    "\n",
    "**Zmienna losowa ciągła** przyjmuje wartości z pewnego przedziału liczb rzeczywistych.\n",
    "\n",
    "Kluczowa konsekwencja:\n",
    "\n",
    "- dla dyskretnej sensowne jest $P(X=x)$ i może być dodatnie,\n",
    "- dla ciągłej zawsze $P(X=x)=0$ — prawdopodobieństwa dotyczą przedziałów (np. $P(a<X<b)$).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "02000022",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>P(X=x)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x    P(X=x)\n",
       "0  1  0.166667\n",
       "1  2  0.166667\n",
       "2  3  0.166667\n",
       "3  4  0.166667\n",
       "4  5  0.166667\n",
       "5  6  0.166667"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(1, 7)\n",
    "p = np.array([1/6] * 6)\n",
    "\n",
    "rozklad_kostki = pd.DataFrame({'x': x, 'P(X=x)': p})\n",
    "rozklad_kostki"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e279afd",
   "metadata": {},
   "source": [
    "### Dla zmiennej ciągłej liczy się przedział, nie punkt\n",
    "\n",
    "W przypadku zmiennej dyskretnej możemy pytać o prawdopodobieństwo konkretnej wartości: na kostce wynik „4” ma sens i dodatnie prawdopodobieństwo. Dla zmiennej ciągłej jest inaczej.\n",
    "\n",
    "Model ciągły zakłada nieskończenie wiele możliwych wartości, więc pojedynczy punkt ma prawdopodobieństwo równe 0. To nie znaczy, że dana okolica jest „niemożliwa”. Znaczy tylko tyle, że musimy mówić językiem przedziałów.\n",
    "\n",
    "Dlatego na wykresach rozkładów ciągłych oś pionowa opisuje **gęstość**, a prawdopodobieństwo odpowiada **polu pod krzywą** na zadanym odcinku."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ca5cffa3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(500 < X < 600) = 0.42148527849205614\n",
      "P(300 < X < 400) = 0.04505375048657056\n",
      "P(X = 550) = 0 (w modelu ciągłym)\n"
     ]
    }
   ],
   "source": [
    "mu = 550\n",
    "sigma = 90\n",
    "\n",
    "x = np.linspace(250, 900, 1200)\n",
    "g = stats.norm.pdf(x, loc=mu, scale=sigma)\n",
    "\n",
    "a1, b1 = 500, 600\n",
    "a2, b2 = 300, 400\n",
    "\n",
    "p_500_600 = stats.norm.cdf(b1, loc=mu, scale=sigma) - stats.norm.cdf(a1, loc=mu, scale=sigma)\n",
    "p_300_400 = stats.norm.cdf(b2, loc=mu, scale=sigma) - stats.norm.cdf(a2, loc=mu, scale=sigma)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(x, g, color='black', linewidth=2)\n",
    "\n",
    "mask1 = (x >= a1) & (x <= b1)\n",
    "mask2 = (x >= a2) & (x <= b2)\n",
    "plt.fill_between(x[mask1], g[mask1], alpha=0.35, label='500-600 ms')\n",
    "plt.fill_between(x[mask2], g[mask2], alpha=0.35, label='300-400 ms')\n",
    "\n",
    "plt.title('Zmienna ciągła: prawdopodobieństwo jako pole pod gęstością')\n",
    "plt.xlabel('Czas reakcji [ms]')\n",
    "plt.ylabel('Gęstość')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "print('P(500 < X < 600) =', p_500_600)\n",
    "print('P(300 < X < 400) =', p_300_400)\n",
    "print('P(X = 550) = 0 (w modelu ciągłym)')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000023",
   "metadata": {},
   "source": [
    "## Wartość oczekiwana i wariancja dla zmiennej dyskretnej: przykład na kostce\n",
    "\n",
    "Dwie podstawowe liczby opisujące rozkład zmiennej losowej:\n",
    "\n",
    "- wartość oczekiwana $\\mathrm{E}[X]$ — długookresowa średnia w wielu powtórzeniach,\n",
    "- wariancja $\\mathrm{Var}(X)$ i odchylenie standardowe $\\mathrm{SD}(X)$ — typowy rozrzut wyników wokół $\\mathrm{E}[X]$.\n",
    "\n",
    "Wzory dla zmiennej dyskretnej:\n",
    "\n",
    "$$\n",
    "\\mathrm{E}[X] = \\sum_x x\\,P(X=x)\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\mathrm{Var}(X) = \\mathrm{E}[(X-\\mathrm{E}[X])^2] = \\mathrm{E}[X^2] - (\\mathrm{E}[X])^2\n",
    "$$\n",
    "\n",
    "Policzmy to dla uczciwej kostki.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "02000024",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E[X] (ze wzoru) = 3.5\n",
      "\n",
      "Var(X) (E[X^2]-(E[X])^2) = 2.916666666666666\n",
      "Var(X) (Σ (x-E[X])^2 p)   = 2.9166666666666665\n",
      "\n",
      "SD(X) = 1.707825127659933\n"
     ]
    }
   ],
   "source": [
    "x = np.arange(1, 7)\n",
    "p = np.array([1/6] * 6)\n",
    "\n",
    "expected = np.sum(x * p)\n",
    "\n",
    "# Dwie równoważne formuły na wariancję\n",
    "expected2 = np.sum((x**2) * p)\n",
    "var_via_ex2 = expected2 - expected**2\n",
    "var_direct = float(np.sum(((x - expected) ** 2) * p))\n",
    "\n",
    "sd = float(np.sqrt(var_direct))\n",
    "\n",
    "print('E[X] (ze wzoru) =', expected)\n",
    "\n",
    "print()\n",
    "print('Var(X) (E[X^2]-(E[X])^2) =', var_via_ex2)\n",
    "print('Var(X) (Σ (x-E[X])^2 p)   =', var_direct)\n",
    "\n",
    "print()\n",
    "print('SD(X) =', sd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "02000025",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E[X] (symulacja): 3.496715\n",
      "Var(X) (symulacja, ddof=0): 2.9100192087749996\n"
     ]
    }
   ],
   "source": [
    "rng = np.random.default_rng(SEED + 1)\n",
    "sample = rng.integers(1, 7, size=200_000)\n",
    "\n",
    "print('E[X] (symulacja):', float(sample.mean()))\n",
    "print('Var(X) (symulacja, ddof=0):', float(sample.var(ddof=0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000027",
   "metadata": {},
   "source": [
    "## Kombinacje i permutacje: liczenie możliwości\n",
    "\n",
    "Często, zanim policzymy prawdopodobieństwo, musimy policzyć \"ile jest możliwości\".\n",
    "To szczególnie ważne przy rozkładzie dwumianowym: pojawia się tam liczba sposobów wyboru, w których próbach wypadł sukces.\n",
    "\n",
    "- **kombinacje**: wybór $k$ elementów z $n$ bez uwzględniania kolejności: $\\binom{n}{k}$,\n",
    "- **permutacje**: wybór z uwzględnianiem kolejności.\n",
    "\n",
    "W Pythonie mamy `math.comb` i `math.perm`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "02000028",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C(10,3) = 120\n",
      "P(10,3) = 720\n"
     ]
    }
   ],
   "source": [
    "n = 10\n",
    "k = 3\n",
    "\n",
    "print('C(10,3) =', math.comb(n, k))\n",
    "print('P(10,3) =', math.perm(n, k))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "072fd57a",
   "metadata": {},
   "source": [
    "## Rozkład dwumianowy: formalny model liczby sukcesów\n",
    "\n",
    "W zadaniu 2AFC naturalnie interesuje nas nie tylko pojedyncza próba, ale także to, ile odpowiedzi poprawnych padnie w całej serii. Jeśli każda próba jest Bernoulliego, prawdopodobieństwo sukcesu jest stałe i próby są niezależne, to liczba sukcesów ma rozkład dwumianowy.\n",
    "\n",
    "Łączą się tu trzy wcześniejsze idee: **definicja próby Bernoulliego**, **liczenie kombinacji** oraz **rachunek prawdopodobieństwa**.\n",
    "\n",
    "Dla $n$ prób i prawdopodobieństwa sukcesu $p$ mamy\n",
    "$$\n",
    "P(X=x)=\\binom{n}{x}p^x(1-p)^{n-x}.\n",
    "$$\n",
    "\n",
    "W praktyce wygodne są też dwie liczby opisujące ten rozkład: wartość oczekiwana i wariancja.\n",
    "$$\n",
    "E[X]=np\n",
    "$$\n",
    "\n",
    "$$\n",
    "Var(X)=np(1-p).\n",
    "$$\n",
    "\n",
    "Pierwsza mówi, gdzie leży średnia liczba sukcesów, druga jak szeroko będą się te wyniki rozrzucać między powtórzeniami."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "9737e3f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>P(X=x)</th>\n",
       "      <th>x * P(X=x)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000341</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.004162</td>\n",
       "      <td>0.004162</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>0.022890</td>\n",
       "      <td>0.045779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>0.074603</td>\n",
       "      <td>0.223809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>0.159568</td>\n",
       "      <td>0.638271</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>0.234033</td>\n",
       "      <td>1.170164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>0.238367</td>\n",
       "      <td>1.430200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>0.166478</td>\n",
       "      <td>1.165348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>0.076303</td>\n",
       "      <td>0.610420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>0.020724</td>\n",
       "      <td>0.186517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10</td>\n",
       "      <td>0.002533</td>\n",
       "      <td>0.025330</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     x    P(X=x)  x * P(X=x)\n",
       "0    0  0.000341    0.000000\n",
       "1    1  0.004162    0.004162\n",
       "2    2  0.022890    0.045779\n",
       "3    3  0.074603    0.223809\n",
       "4    4  0.159568    0.638271\n",
       "5    5  0.234033    1.170164\n",
       "6    6  0.238367    1.430200\n",
       "7    7  0.166478    1.165348\n",
       "8    8  0.076303    0.610420\n",
       "9    9  0.020724    0.186517\n",
       "10  10  0.002533    0.025330"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Suma prawdopodobieństw: 1.0000000000000002\n",
      "E[X] (ze wzoru np): 5.5\n",
      "Var(X) (ze wzoru np(1-p)): 2.4749999999999996\n"
     ]
    }
   ],
   "source": [
    "n = 10\n",
    "p = 0.55\n",
    "x = np.arange(0, n + 1)\n",
    "pmf = stats.binom.pmf(x, n=n, p=p)\n",
    "\n",
    "rozklad_dwumianowy = pd.DataFrame(\n",
    "    {\n",
    "        'x': x,\n",
    "        'P(X=x)': pmf,\n",
    "        'x * P(X=x)': x * pmf,\n",
    "    }\n",
    ")\n",
    "\n",
    "display(rozklad_dwumianowy)\n",
    "\n",
    "print('Suma prawdopodobieństw:', float(pmf.sum()))\n",
    "print('E[X] (ze wzoru np):', n * p)\n",
    "print('Var(X) (ze wzoru np(1-p)):', n * p * (1 - p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "8878895c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9, 4))\n",
    "plt.bar(x, pmf, color='lightgrey', edgecolor='white')\n",
    "plt.title('Rozkład dwumianowy: liczba poprawnych odpowiedzi w 10 próbach')\n",
    "plt.xlabel('Liczba sukcesów')\n",
    "plt.ylabel('Prawdopodobieństwo')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88df0252",
   "metadata": {},
   "source": [
    "### Jak zmienia się kształt rozkładu dwumianowego\n",
    "\n",
    "Dla ustalonej liczby prób rozkład jest najbardziej symetryczny, gdy $p$ jest bliskie 0.5. Gdy $p$ oddala się od 0.5, rozkład robi się coraz bardziej skośny.\n",
    "\n",
    "Z kolei przy większym $n$ rozkład zwykle wygląda bardziej „gładko” i bywa dobrze przybliżany rozkładem normalnym, o ile zarówno $np$, jak i $n(1-p)$ nie są zbyt małe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "7ecfcd4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x300 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E[X] teoria = 14.0 | symulacja = 13.998285\n",
      "Var(X) teoria = 4.200000000000001 | symulacja = 4.2011520587749995\n"
     ]
    }
   ],
   "source": [
    "x10 = np.arange(0, 11)\n",
    "p_values = [0.60, 0.30, 0.05]\n",
    "\n",
    "fig, axes = plt.subplots(1, 3, figsize=(12, 3), sharey=True)\n",
    "for ax, p_loc in zip(axes, p_values):\n",
    "    pmf_loc = stats.binom.pmf(x10, n=10, p=p_loc)\n",
    "    ax.bar(x10, pmf_loc, color='lightgrey', edgecolor='white')\n",
    "    ax.set_title(f'n=10, p={p_loc:.2f}')\n",
    "    ax.set_xlabel('Liczba sukcesów')\n",
    "axes[0].set_ylabel('Prawdopodobieństwo')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "rng = np.random.default_rng(SEED + 40)\n",
    "n = 20\n",
    "p = 0.70\n",
    "proby = rng.binomial(n=n, p=p, size=200_000)\n",
    "\n",
    "print('E[X] teoria =', n * p, '| symulacja =', float(proby.mean()))\n",
    "print('Var(X) teoria =', n * p * (1 - p), '| symulacja =', float(proby.var(ddof=0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000029",
   "metadata": {},
   "source": [
    "## Twierdzenie Bayesa i myślenie w naturalnych częstościach\n",
    "\n",
    "Twierdzenie Bayesa pozwala „odwrócić” warunkowanie — czyli przejść od $P(B\\mid A)$ do $P(A\\mid B)$. Tożsamość wynika z definicji prawdopodobieństwa warunkowego.\n",
    "\n",
    "$$\n",
    "P(A\\mid B) = \\frac{P(B\\mid A)\\,P(A)}{P(B)}\n",
    "$$\n",
    "\n",
    "W praktyce bardzo pomaga podejście **naturalnych częstości**: zamiast pracować na ułamkach, przeliczamy je na liczby w hipotetycznej populacji (np. 10 000 prób).\n",
    "\n",
    "Przykład z kognitywistyki: detekcja słabego bodźca.\n",
    "\n",
    "- Z pewnym prawdopodobieństwem w próbie **jest bodziec** (a w pozostałych próbach go nie ma).\n",
    "- Badany odpowiada „tak, był bodziec” albo „nie, nie było”.\n",
    "- Łatwo pomylić $P(\\text{tak}\\mid\\text{bodziec})$ z $P(\\text{bodziec}\\mid\\text{tak})$.\n",
    "\n",
    "Policzymy $P(\\text{bodziec}\\mid\\text{odpowiedź tak})$ na dwa sposoby: przez naturalne częstości i ze wzoru Bayesa.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "02000030",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>warunek</th>\n",
       "      <th>liczba prób</th>\n",
       "      <th>odpowiedź \"tak\" (liczba)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>bodziec</td>\n",
       "      <td>100</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>brak bodźca</td>\n",
       "      <td>9900</td>\n",
       "      <td>495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>razem</td>\n",
       "      <td>10000</td>\n",
       "      <td>585</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       warunek  liczba prób  odpowiedź \"tak\" (liczba)\n",
       "0      bodziec          100                        90\n",
       "1  brak bodźca         9900                       495\n",
       "2        razem        10000                       585"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Przykład: detekcja bodźca i odpowiedź \"tak/nie\"\n",
    "\n",
    "p_bodziec = 0.01                 # P(bodziec)\n",
    "p_tak_gdy_bodziec = 0.90         # P(odpowiedź \"tak\" | bodziec)\n",
    "p_tak_gdy_brak_bodzca = 0.05     # P(odpowiedź \"tak\" | brak bodźca)\n",
    "\n",
    "liczba_prob = 10_000\n",
    "\n",
    "n_bodziec = int(liczba_prob * p_bodziec)\n",
    "n_brak_bodzca = liczba_prob - n_bodziec\n",
    "\n",
    "trafienia = int(round(n_bodziec * p_tak_gdy_bodziec))\n",
    "falszywe_alarmy = int(round(n_brak_bodzca * p_tak_gdy_brak_bodzca))\n",
    "razem_tak = trafienia + falszywe_alarmy\n",
    "\n",
    "p_bodziec_gdy_tak_freq = trafienia / razem_tak\n",
    "\n",
    "tabela = pd.DataFrame(\n",
    "    {\n",
    "        'warunek': ['bodziec', 'brak bodźca', 'razem'],\n",
    "        'liczba prób': [n_bodziec, n_brak_bodzca, liczba_prob],\n",
    "        'odpowiedź \"tak\" (liczba)': [trafienia, falszywe_alarmy, razem_tak],\n",
    "    }\n",
    ")\n",
    "\n",
    "tabela"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "02000031",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(bodziec | odpowiedź \"tak\") (naturalne częstości): 0.15384615384615385\n",
      "P(bodziec | odpowiedź \"tak\") (Bayes): 0.15384615384615385\n"
     ]
    }
   ],
   "source": [
    "print('P(bodziec | odpowiedź \"tak\") (naturalne częstości):', p_bodziec_gdy_tak_freq)\n",
    "\n",
    "# To samo ze wzoru Bayesa\n",
    "p_tak = p_tak_gdy_bodziec * p_bodziec + p_tak_gdy_brak_bodzca * (1 - p_bodziec)\n",
    "p_bodziec_gdy_tak_bayes = (p_tak_gdy_bodziec * p_bodziec) / p_tak\n",
    "\n",
    "print('P(bodziec | odpowiedź \"tak\") (Bayes):', p_bodziec_gdy_tak_bayes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "02000032",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(bodziec | odpowiedź \"tak\") (symulacja): 0.15446330546406553\n"
     ]
    }
   ],
   "source": [
    "# Weryfikacja symulacyjna\n",
    "rng = np.random.default_rng(SEED + 4)\n",
    "n = 200_000\n",
    "\n",
    "bodziec_obecny = rng.random(n) < p_bodziec\n",
    "\n",
    "odpowiedz_tak = np.zeros(n, dtype=bool)\n",
    "\n",
    "los = rng.random(n)\n",
    "odpowiedz_tak[bodziec_obecny] = los[bodziec_obecny] < p_tak_gdy_bodziec\n",
    "\n",
    "los = rng.random(n)\n",
    "odpowiedz_tak[~bodziec_obecny] = los[~bodziec_obecny] < p_tak_gdy_brak_bodzca\n",
    "\n",
    "p_bodziec_gdy_tak_mc = float(np.mean(bodziec_obecny & odpowiedz_tak) / np.mean(odpowiedz_tak))\n",
    "print('P(bodziec | odpowiedź \"tak\") (symulacja):', p_bodziec_gdy_tak_mc)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000033",
   "metadata": {},
   "source": [
    "### Widżet: Bayes w naturalnych częstościach (detekcja bodźca)\n",
    "\n",
    "Zmieniaj częstość bodźca oraz parametry odpowiedzi i obserwuj, jak zmienia się $P(\\text{bodziec} \\mid \\text{odpowiedź tak})$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "02000034",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "701349312e2642128bb1d49dd8da2dd2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(FloatSlider(value=0.01, description='P(bodziec)', max=0.2, readout_format='.3f', step=0.005), F…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2fdc26285de746eab2e7f80b0fd4360c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output(outputs=({'name': 'stdout', 'text': 'P(bodziec | odpowiedź \"tak\") = 0.15384615384615385\\n', 'output_typ…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if not WIDGETY_DOSTEPNE:\n",
    "    print('Widżety nie są dostępne: zainstaluj pakiet ipywidgets, aby korzystać z części interaktywnych.')\n",
    "else:\n",
    "    p_bodziec_slider = widgets.FloatSlider(\n",
    "        value=0.01,\n",
    "        min=0.0,\n",
    "        max=0.2,\n",
    "        step=0.005,\n",
    "        description='P(bodziec)',\n",
    "        readout_format='.3f',\n",
    "    )\n",
    "    p_tak_gdy_bodziec_slider = widgets.FloatSlider(\n",
    "        value=0.90,\n",
    "        min=0.50,\n",
    "        max=1.00,\n",
    "        step=0.01,\n",
    "        description='P(tak|bodziec)',\n",
    "        readout_format='.2f',\n",
    "    )\n",
    "    p_tak_gdy_brak_slider = widgets.FloatSlider(\n",
    "        value=0.05,\n",
    "        min=0.00,\n",
    "        max=0.50,\n",
    "        step=0.01,\n",
    "        description='P(tak|brak)',\n",
    "        readout_format='.2f',\n",
    "    )\n",
    "    liczba_prob_slider = widgets.IntSlider(\n",
    "        value=10000,\n",
    "        min=1000,\n",
    "        max=50000,\n",
    "        step=1000,\n",
    "        description='Liczba prób',\n",
    "    )\n",
    "\n",
    "    def pokaz_bayes(p_bodziec, p_tak_gdy_bodziec, p_tak_gdy_brak_bodzca, liczba_prob):\n",
    "        n_bodziec = int(round(liczba_prob * p_bodziec))\n",
    "        n_brak_bodzca = liczba_prob - n_bodziec\n",
    "\n",
    "        trafienia = int(round(n_bodziec * p_tak_gdy_bodziec))\n",
    "        falszywe_alarmy = int(round(n_brak_bodzca * p_tak_gdy_brak_bodzca))\n",
    "        razem_tak = trafienia + falszywe_alarmy\n",
    "\n",
    "        if razem_tak == 0:\n",
    "            print('Przy tych parametrach nie ma odpowiedzi „tak”.')\n",
    "            return\n",
    "\n",
    "        p_bodziec_gdy_tak = trafienia / razem_tak\n",
    "        print('P(bodziec | odpowiedź \"tak\") =', p_bodziec_gdy_tak)\n",
    "\n",
    "        tabela = pd.DataFrame(\n",
    "            {\n",
    "                'warunek': ['bodziec', 'brak bodźca', 'razem'],\n",
    "                'liczba prób': [n_bodziec, n_brak_bodzca, liczba_prob],\n",
    "                'odpowiedź \"tak\" (liczba)': [trafienia, falszywe_alarmy, razem_tak],\n",
    "            }\n",
    "        )\n",
    "        display(tabela)\n",
    "\n",
    "        plt.figure(figsize=(6, 3))\n",
    "        plt.bar(\n",
    "            ['bodziec', 'brak bodźca'],\n",
    "            [trafienia, falszywe_alarmy],\n",
    "            color=['#4C78A8', '#F58518'],\n",
    "            edgecolor='white',\n",
    "        )\n",
    "        plt.title('Skład odpowiedzi „tak”')\n",
    "        plt.ylabel('Liczba')\n",
    "        plt.show()\n",
    "\n",
    "    out = widgets.interactive_output(\n",
    "        pokaz_bayes,\n",
    "        {\n",
    "            'p_bodziec': p_bodziec_slider,\n",
    "            'p_tak_gdy_bodziec': p_tak_gdy_bodziec_slider,\n",
    "            'p_tak_gdy_brak_bodzca': p_tak_gdy_brak_slider,\n",
    "            'liczba_prob': liczba_prob_slider,\n",
    "        },\n",
    "    )\n",
    "\n",
    "    display(\n",
    "        widgets.VBox(\n",
    "            [\n",
    "                p_bodziec_slider,\n",
    "                p_tak_gdy_bodziec_slider,\n",
    "                p_tak_gdy_brak_slider,\n",
    "                liczba_prob_slider,\n",
    "            ]\n",
    "        ),\n",
    "        out,\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4f41d59",
   "metadata": {},
   "source": [
    "## Dwie pułapki intuicji probabilistycznej\n",
    "\n",
    "W praktyce najtrudniejsze bywa nie samo liczenie, tylko utrzymanie właściwej interpretacji. Dwie pomyłki pojawiają się wyjątkowo często: przekonanie, że los „musi się wyrównać” w krótkim czasie, oraz ignorowanie częstości bazowej zdarzeń rzadkich.\n",
    "\n",
    "Obie pułapki warto pokazać na krótkiej symulacji, bo liczby zwykle przekonują szybciej niż deklaracje."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21675084",
   "metadata": {},
   "source": [
    "### Pułapka 1: błąd hazardzisty (*gambler's fallacy*)\n",
    "\n",
    "Jeśli w serii rzutów kilka razy z rzędu wypadnie orzeł, intuicja często podpowiada, że „teraz już powinna wypaść reszka”. To błąd.\n",
    "\n",
    "W modelu niezależnych rzutów prawdopodobieństwo reszki w kolejnym rzucie pozostaje takie samo niezależnie od historii. Seria może być psychologicznie zaskakująca, ale nie zmienia mechanizmu losowania."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "c68dc6d9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(reszka na 6. rzucie | 5 orłów wcześniej) ≈ 0.5095040883508548\n",
      "Wartość odniesienia dla uczciwej monety: 0.5\n"
     ]
    }
   ],
   "source": [
    "rng = np.random.default_rng(SEED + 50)\n",
    "n_sim = 300_000\n",
    "\n",
    "# 1 = orzeł, 0 = reszka\n",
    "rzuty = rng.integers(0, 2, size=(n_sim, 6))\n",
    "warunek_5_orlow = (rzuty[:, :5] == 1).all(axis=1)\n",
    "\n",
    "p_reszka_po_5_orlach = np.mean(rzuty[warunek_5_orlow, 5] == 0)\n",
    "\n",
    "print('P(reszka na 6. rzucie | 5 orłów wcześniej) ≈', p_reszka_po_5_orlach)\n",
    "print('Wartość odniesienia dla uczciwej monety: 0.5')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27674f30",
   "metadata": {},
   "source": [
    "### Pułapka 2: zaniedbanie częstości bazowej (*base-rate neglect*)\n",
    "\n",
    "W zadaniach diagnostycznych łatwo przecenić „siłę” pojedynczego dodatniego wyniku testu. Nawet czuły test (test dla którego $P(\\text{wynik dodatni} \\mid \\text{choroba})$ jest wysokie) może dawać zaskakująco małe $P(\\text{choroba} \\mid \\text{wynik dodatni})$, jeśli sama choroba jest rzadka.\n",
    "\n",
    "To klasyczny przypadek, w którym Bayes porządkuje intuicję: wynik testu trzeba zawsze czytać razem z częstością bazową zjawiska.\n",
    "\n",
    "Załóżmy, że prawdopodobieństwo pozytywnego wyniku testu, gdy ktoś jest jest rzeczywiści echory wynosi $0.8$. Ta wartość to czułość testu. Jakie jest prawdopodobieństwo tego, że ktoś jest chory, gdy wynik testu wyszedł dodatni? Nie jest to wcale $0.8$. Wartość ta zależy od tego jak rzadka jest choroba w populacji i jak często test daje nam wynik ujemy w sytuacji braku choroby."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "0218ea60",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(choroba | wynik dodatni) = 0.07763975155279504\n"
     ]
    }
   ],
   "source": [
    "p_choroba = 0.01\n",
    "p_dodatni_gdy_choroba = 0.80\n",
    "p_dodatni_gdy_brak_choroby = 0.096\n",
    "\n",
    "p_dodatni = p_dodatni_gdy_choroba * p_choroba + p_dodatni_gdy_brak_choroby * (1 - p_choroba)\n",
    "p_choroba_gdy_dodatni = (p_dodatni_gdy_choroba * p_choroba) / p_dodatni\n",
    "\n",
    "print('P(choroba | wynik dodatni) =', p_choroba_gdy_dodatni)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000038",
   "metadata": {},
   "source": [
    "## Ćwiczenia\n",
    "\n",
    "1) Dwie kostki i reguły działań na zdarzeniach.\n",
    "\n",
    "- Oblicz $P(\\text{suma}=9)$ metodą enumeracji.\n",
    "- Oblicz $P(\\text{suma}=9 \\cup \\text{przynajmniej jedna 6})$ i jawnie zweryfikuj regułę dodawania.\n",
    "- (Opcjonalnie) Porównaj wynik dokładny z symulacją Monte Carlo.\n",
    "\n",
    "2) Warunkowanie i interpretacja.\n",
    "\n",
    "- Policz $P(\\text{suma}=7 \\mid \\text{pierwszy rzut parzysty})$.\n",
    "- Zapisz własnymi słowami, co dokładnie oznacza to prawdopodobieństwo i jaki jest zbiór odniesienia.\n",
    "\n",
    "3) Dyskretna kontra ciągła.\n",
    "\n",
    "- Dla modelu normalnego policz $P(500 < X < 600)$ oraz $P(300 < X < 400)$.\n",
    "- Wyjaśnij, dlaczego $P(X=550)=0$ nie stoi w sprzeczności z tym, że wartości „w okolicy 550” są częste.\n",
    "\n",
    "4) Rozkład dwumianowy jako model 2AFC.\n",
    "\n",
    "- Dla $n=10$ i $p=0.55$ policz $P(X=7)$ i zinterpretuj słownie wynik.\n",
    "- Sprawdź, jak zmienia się kształt rozkładu przy $p=0.60$, $p=0.30$ i $p=0.05$.\n",
    "- Zweryfikuj symulacyjnie wzory $E[X]=np$ i $Var(X)=np(1-p)$.\n",
    "\n",
    "5) Bayes i częstość bazowa.\n",
    "\n",
    "- Zmień `p_bodziec` na 0.05 i policz ponownie $P(\\\\text{bodziec} \\mid \\\\text{odpowiedź tak})$.\n",
    "- Porównaj wynik z symulacją i opisz, jak częstość bazowa wpływa na interpretację dodatniej odpowiedzi.\n",
    "\n",
    "6) Pułapki intuicji.\n",
    "\n",
    "- Uruchom symulację z błędem gracza i wyjaśnij, dlaczego seria wcześniejszych wyników nie zmienia prawdopodobieństwa w kolejnym rzucie.\n",
    "- W przykładzie diagnostycznym zmień odsetek fałszywie dodatnich na 0.05 i porównaj nowy wynik z poprzednim."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02000039",
   "metadata": {},
   "source": [
    "## Podsumowanie\n",
    "\n",
    "- W podejściu częstotliwościowym prawdopodobieństwo interpretujemy jako stabilizującą się częstość w długiej serii powtórzeń, ale świadomie odróżniamy też język analityczny i subiektywny.\n",
    "- Umiesz rozróżniać prawdopodobieństwo zwykłe, łączne i warunkowe oraz czytać je poprawnie w kontekście tej samej tabeli danych.\n",
    "- Wiesz, dlaczego niezależność nie jest automatyczna i jak zmienia się rachunek przy losowaniu bez zwracania.\n",
    "- Rozumiesz różnicę między zmienną dyskretną i ciągłą: dla ciągłej liczymy prawdopodobieństwa przedziałów jako pola pod gęstością.\n",
    "- Znasz rozkład dwumianowy jako model liczby sukcesów w próbach Bernoulliego oraz potrafisz interpretować jego parametry $E[X]=np$ i $Var(X)=np(1-p)$.\n",
    "- Umiesz zastosować Bayesa w kategoriach naturalnych częstości i identyfikować typowe pułapki intuicji, takie jak błąd gracza i zaniedbanie częstości bazowej."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.14.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}