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    "## Bonus Exercise: Bayes' Rule\n",
    "### Description\n",
    "In this exercise, you will implement Bayes' rule to solve a simple card game."
   ],
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    "import random\n",
    "\n",
    "class CardDeck:\n",
    "    def __init__(self):\n",
    "        # Initialize the deck of cards\n",
    "        self.cards = ['R', 'R', 'B', 'B']\n",
    "        # Shuffle the deck of cards\n",
    "        random.shuffle(self.cards)\n",
    "        # Initialize the prior probability\n",
    "        <code>\n",
    "\n",
    "    def draw_card(self, index):\n",
    "        \"\"\"\n",
    "        Draw a card from the deck\n",
    "        :param index: the index of the card to be drawn\n",
    "        :return: the card and its color\n",
    "        \"\"\"\n",
    "        card = self.cards.pop(index)\n",
    "        color = 'Red' if card == 'R' else 'Black'\n",
    "        return (card, color)\n",
    "\n",
    "    def get_card_color(self, index):\n",
    "        \"\"\"\n",
    "        Get the color of a card\n",
    "        :return: the color of the card\n",
    "        \"\"\"\n",
    "        card = self.cards[index]\n",
    "        color = 'Red' if card == 'R' else 'Black'\n",
    "        return color\n",
    "\n",
    "    def get_remainder(self):\n",
    "        \"\"\"\n",
    "        Get the remainder deck\n",
    "        :return: the remainder deck\n",
    "        \"\"\"\n",
    "        return self.cards\n",
    "\n",
    "    \"\"\"\n",
    "    Update the prior probability based on Bayes' rule\n",
    "    function name: update_probabilities\n",
    "    \"\"\"\n",
    "    ### function missing here\n",
    "    <code>\n",
    "    \"\"\"\n",
    "    Calculate the posterior probability based on the prior probability, likelihood, and marginal likelihood\n",
    "    function name: get_posterior\n",
    "    \"\"\"\n",
    "    ### function missing here\n",
    "    <code>\n",
    "\n",
    "    def play_game(self):\n",
    "        while self.cards:\n",
    "            for i, card in enumerate(self.cards):\n",
    "                print(f'{i}: Unknown')\n",
    "             # only one card left\n",
    "            if len(self.cards) == 1:\n",
    "                # code missing here\n",
    "                <code>\n",
    "                self.cards.pop()\n",
    "            else:\n",
    "                index = int(input(f\"Remainder deck: {self.get_remainder()}\\nEnter the index of the card you want to draw:\"))\n",
    "                card, color = self.draw_card(index-1)\n",
    "                print(f'You drew a {color} card with value {card}')\n",
    "\n",
    "                # Calculate the likelihood and marginal likelihood based on the color of the drawn card\n",
    "                <code>\n",
    "            # Update the prior probability based on Bayes' rule\n",
    "            <code>\n",
    "            # Print the posterior probabilities\n",
    "            print(f\"After drawing a {card} card:\")\n",
    "            print(f\"The probability that the other card is red: {posterior_red:.2f}\")\n",
    "            print(f\"The probability that the other card is black: {posterior_black:.2f}\")\n",
    "        print(\"The deck is empty.\")\n",
    "\n",
    "\n"
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   "source": [
    "play the game by running the following code:\n"
   ],
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     "text": [
      "0: Unknown\n",
      "1: Unknown\n",
      "2: Unknown\n",
      "3: Unknown\n",
      "You drew a Red card with value R\n",
      "After drawing a R card:\n",
      "The probability that the other card is red: 0.33\n",
      "The probability that the other card is black: 0.67\n",
      "0: Unknown\n",
      "1: Unknown\n",
      "2: Unknown\n",
      "You drew a Black card with value B\n",
      "After drawing a B card:\n",
      "The probability that the other card is red: 0.33\n",
      "The probability that the other card is black: 0.67\n",
      "0: Unknown\n",
      "1: Unknown\n"
     ]
    }
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   "source": [
    "deck = CardDeck()\n",
    "deck.play_game()\n"
   ],
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