193 lines
5.6 KiB
Plaintext
193 lines
5.6 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"source": [
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"## Bonus Exercise: Bayes' Rule\n",
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"### Description\n",
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"In this exercise, you will implement Bayes' rule to solve a simple card game."
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],
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{
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"cell_type": "code",
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"execution_count": 1,
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"outputs": [],
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"source": [
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"import random\n",
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"\n",
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"class CardDeck:\n",
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" def __init__(self):\n",
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" # Initialize the deck of cards\n",
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" self.cards = ['R', 'R', 'B', 'B']\n",
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" # Shuffle the deck of cards\n",
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" random.shuffle(self.cards)\n",
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" # Initialize the prior probability\n",
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"\n",
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" # code missing here\n",
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"\n",
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"\n",
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" def draw_card(self, index):\n",
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" \"\"\"\n",
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" Draw a card from the deck\n",
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" :param index: the index of the card to be drawn\n",
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" :return: the card and its color\n",
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" \"\"\"\n",
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" card = self.cards.pop(index)\n",
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" color = 'Red' if card == 'R' else 'Black'\n",
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" return (card, color)\n",
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"\n",
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" def get_card_color(self, index):\n",
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" \"\"\"\n",
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" Get the color of a card\n",
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" :return: the color of the card\n",
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" \"\"\"\n",
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" card = self.cards[index]\n",
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" color = 'Red' if card == 'R' else 'Black'\n",
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" return color\n",
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"\n",
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" def get_remainder(self):\n",
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" \"\"\"\n",
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" Get the remainder deck\n",
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" :return: the remainder deck\n",
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" \"\"\"\n",
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" return self.cards\n",
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"\n",
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" \"\"\"\n",
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" Update the prior probability based on Bayes' rule\n",
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" function name: update_probabilities\n",
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" \"\"\"\n",
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" ### function missing here\n",
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" \"\"\"\n",
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" Calculate the posterior probability based on the prior probability, likelihood, and marginal likelihood\n",
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" function name: get_posterior\n",
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" \"\"\"\n",
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" ### function missing here\n",
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"\n",
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" def play_game(self):\n",
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" while self.cards:\n",
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" for i, card in enumerate(self.cards):\n",
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" print(f'{i}: Unknown')\n",
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" # only one card left\n",
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" if len(self.cards) == 1:\n",
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" # code missing here\n",
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" self.cards.pop()\n",
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" else:\n",
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" index = int(input(f\"Remainder deck: {self.get_remainder()}\\nEnter the index of the card you want to draw:\"))\n",
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" card, color = self.draw_card(index-1)\n",
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" print(f'You drew a {color} card with value {card}')\n",
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"\n",
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" # Calculate the likelihood and marginal likelihood based on the color of the drawn card\n",
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"\n",
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" # Update the prior probability based on Bayes' rule\n",
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" # code missing here\n",
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" posterior_red = 0 # you must calculate this value\n",
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" posterior_black = 0 # you must calculate this value\n",
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" # Print the posterior probabilities\n",
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" print(f\"After drawing a {card} card:\")\n",
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" print(f\"The probability that the other card is red: {posterior_red:.2f}\")\n",
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" print(f\"The probability that the other card is black: {posterior_black:.2f}\")\n",
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" print(\"The deck is empty.\")\n",
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"\n",
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"\n"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"play the game by running the following code:\n"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0: Unknown\n",
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"1: Unknown\n",
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"2: Unknown\n",
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"3: Unknown\n",
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"You drew a Black card with value B\n",
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"After drawing a B card:\n",
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"The probability that the other card is red: 0.00\n",
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"The probability that the other card is black: 0.00\n",
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"0: Unknown\n",
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"1: Unknown\n",
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"2: Unknown\n",
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"You drew a Red card with value R\n",
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"After drawing a R card:\n",
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"The probability that the other card is red: 0.00\n",
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"The probability that the other card is black: 0.00\n",
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"0: Unknown\n",
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"1: Unknown\n",
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"You drew a Red card with value R\n",
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"After drawing a R card:\n",
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"The probability that the other card is red: 0.00\n",
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"The probability that the other card is black: 0.00\n",
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"0: Unknown\n",
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"After drawing a B card:\n",
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"The probability that the other card is red: 0.00\n",
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"The probability that the other card is black: 0.00\n",
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"The deck is empty.\n"
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]
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}
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],
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"source": [
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"deck = CardDeck()\n",
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"deck.play_game()\n"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"display_name": "Python 3",
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"language": "python",
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