update Monty Hall

907c980b · Ulrich Kerzel · bb8feeb9 · 907c980b
Commit 907c980b authored 4 months ago by Ulrich Kerzel
--- a/datascienceintro/solutions/Solution_MontyHall.ipynb
+++ b/datascienceintro/solutions/Solution_MontyHall.ipynb
 {
-  "nbformat": 4,
-  "nbformat_minor": 0,
-  "metadata": {
-    "colab": {
-      "provenance": []
-    },
-    "kernelspec": {
-      "name": "python3",
-      "display_name": "Python 3"
-    },
-    "language_info": {
-      "name": "python"
-    }
-  },
  "cells": [
    {
      "cell_type": "markdown",
+      "metadata": {
+        "id": "aQVYzt-A7so-"
+      },
      "source": [
        "# Monty Hall\n",
        "\n",
@@ -25,21 +14,18 @@
        "The host of the show lets the contestant make an initial choice, then opens one of the doors (not the one the contestant has chosen) and then offers the contestant the choice to switch doors.\n",
        "\n",
        "Is it beneficial to switch the doors?"
-      ],
-      "metadata": {
-        "id": "aQVYzt-A7so-"
-      }
+      ]
    },
    {
      "cell_type": "code",
-      "source": [
-        "import random"
-      ],
+      "execution_count": 1,
      "metadata": {
        "id": "KuoDvxxe8F3M"
      },
-      "execution_count": 1,
-      "outputs": []
+      "outputs": [],
+      "source": [
+        "import random"
+      ]
    },
    {
      "cell_type": "code",
@@ -90,14 +76,7 @@
    },
    {
      "cell_type": "code",
-      "source": [
-        "num_trials = 5000\n",
-        "stay_win_rate, switch_win_rate = monty_hall_simulation(num_trials=num_trials)\n",
-        "\n",
-        "print(f\"After {num_trials} trials:\")\n",
-        "print(f\"Winning by staying with the initial choice: \\t {stay_win_rate*100:.2f}%\")\n",
-        "print(f\"Winning by switching to the other door: \\t {switch_win_rate*100:.2f}%\")"
-      ],
+      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
@@ -105,18 +84,41 @@
        "id": "YOPqK0rd8Q5r",
        "outputId": "cb585501-1540-46d3-a6e1-e504021f2015"
      },
-      "execution_count": 12,
      "outputs": [
        {
-          "output_type": "stream",
          "name": "stdout",
+          "output_type": "stream",
          "text": [
            "After 5000 trials:\n",
            "Winning by staying with the initial choice: \t 32.60%\n",
            "Winning by switching to the other door: \t 67.40%\n"
          ]
        }
+      ],
+      "source": [
+        "num_trials = 5000\n",
+        "stay_win_rate, switch_win_rate = monty_hall_simulation(num_trials=num_trials)\n",
+        "\n",
+        "print(f\"After {num_trials} trials:\")\n",
+        "print(f\"Winning by staying with the initial choice: \\t {stay_win_rate*100:.2f}%\")\n",
+        "print(f\"Winning by switching to the other door: \\t {switch_win_rate*100:.2f}%\")"
      ]
    }
-  ]
+  ],
+  "metadata": {
+    "colab": {
+      "provenance": []
+    },
+    "kernelspec": {
+      "display_name": "datascienceintro-eVBNPtpL-py3.11",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "name": "python",
+      "version": "3.11.11"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
 }
 %% Cell type:markdown id: tags:

 # Monty Hall

 In this puzzle, a contestant in a game-show gets to choose between 3 doors.
 Behind one of the doors, a prize (the "car") is hidden, the other two doors do not win (the "goat").

 The host of the show lets the contestant make an initial choice, then opens one of the doors (not the one the contestant has chosen) and then offers the contestant the choice to switch doors.

 Is it beneficial to switch the doors?

 %% Cell type:code id: tags:

-``` 
+``` python
 import random
 ```

 %% Cell type:code id: tags:

-``` 
+``` python

 def monty_hall_simulation(num_trials=5000):
    stay_wins = 0
    switch_wins = 0

    for _ in range(num_trials):
        # Randomly place the car behind one of the three doors
        car_door = random.randint(1, 3)
        # Contestant makes an initial choice randomly
        contestant_choice = random.randint(1, 3)

        # Host opens a door
        possible_doors = [1, 2, 3]
        # Host cannot open the door with the car or the contestant's choice
        doors_host_can_open = [door for door in possible_doors
                               if
                               door != car_door and
                               door != contestant_choice]
        host_opened_door = random.choice(doors_host_can_open)

        # Determine the other door that the contestant can switch to
        remaining_door = [door for door in possible_doors
                          if
                          door != contestant_choice and
                          door != host_opened_door][0]

        # If the contestant stays with their initial choice
        if contestant_choice == car_door:
            stay_wins += 1
        # If the contestant switches to the remaining door
        elif remaining_door == car_door:
            switch_wins += 1

    stay_win_rate = stay_wins / num_trials
    switch_win_rate = switch_wins / num_trials

    return stay_win_rate, switch_win_rate
 ```

 %% Cell type:code id: tags:

-``` 
+``` python
 num_trials = 5000
 stay_win_rate, switch_win_rate = monty_hall_simulation(num_trials=num_trials)

 print(f"After {num_trials} trials:")
 print(f"Winning by staying with the initial choice: \t {stay_win_rate*100:.2f}%")
 print(f"Winning by switching to the other door: \t {switch_win_rate*100:.2f}%")
 ```

 %% Output

    After 5000 trials:
    Winning by staying with the initial choice: 	 32.60%
    Winning by switching to the other door: 	 67.40%