{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# MAT-204:00010 - Probability\n", "Author: Thanawin Pattanaphol - Date: 23th December 2024 - Description: Basic probability calculations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Importing Libraries" ] }, { "cell_type": "code", "execution_count": 281, "metadata": {}, "outputs": [], "source": [ "import pandas as pd \n", "from matplotlib_venn import venn3\n", "from matplotlib import pyplot as plt \n", "\n", "Dat = pd.read_csv('DataLoL.csv')\n", "\n", "num_games = len(Dat)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Questions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Probability: Blue Team wins" ] }, { "cell_type": "code", "execution_count": 282, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Probability that Blue Team wins: 0.4990383642069035\n" ] } ], "source": [ "# Calculating the probability by diving the amount of games that blue won\n", "# dividing it by the amount of total games\n", "# Thus: p = Number of time an event occurs / Total nmumber of possible events\n", "prob_blue_wins = len(Dat[Dat['blueWins'] == 1]) / num_games\n", "print(\"Probability that Blue Team wins:\", prob_blue_wins)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Probability: Blue Team wins and kills the dragon" ] }, { "cell_type": "code", "execution_count": 283, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Probability that Blue Team wins and kills the dragon: 0.23200728818706348\n" ] } ], "source": [ "# Doing a similar calculation with the difference being\n", "# the number of time an event occurs now only counts\n", "# the number of times blue team wins and kills the dragon\n", "\n", "prob_blue_wins_dragons = len(Dat[(Dat['blueWins'] == 1) & (Dat['blueDragons'] == 1)]) / num_games\n", "print(\"Probability that Blue Team wins and kills the dragon:\", prob_blue_wins_dragons)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Probability: Blue Team wins and kills the herald" ] }, { "cell_type": "code", "execution_count": 284, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Probability that Blue Team wins and kills the herald: 0.11185342646016803\n" ] } ], "source": [ "# Similar calculation but with the number of events that\n", "# team blue wins and kills the herald\n", "\n", "prob_blue_wins_heralds = len(Dat[(Dat['blueWins'] == 1) & (Dat['blueHeralds'] == 1)]) / num_games\n", "print(\"Probability that Blue Team wins and kills the herald:\", prob_blue_wins_heralds)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Count: All possible cases (Venn Diagram)" ] }, { "cell_type": "code", "execution_count": 285, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Declaring variable for each set\n", "# Loop through the whole games dataset and if the item-\n", "# -matches the condition, add it to the set for that\n", "# condition list\n", "\n", "game_blue_wins = set()\n", "game_blue_dragon = set()\n", "game_blue_herald = set()\n", "\n", "for game in range(num_games):\n", " if(Dat['blueWins'][game] == 1):\n", " game_blue_wins.add(game)\n", " if(Dat['blueDragons'][game] == 1):\n", " game_blue_dragon.add(game)\n", " if(Dat['blueHeralds'][game] == 1):\n", " game_blue_herald.add(game)\n", "\n", "venn3([game_blue_wins, game_blue_dragon, game_blue_herald], ('A', 'B', 'C'))\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Probability: Each possible events (Venn Diagram)" ] }, { "cell_type": "code", "execution_count": 286, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Setting the variable for each section of the venn diagram\n", "# Use these values to calculate its probability by\n", "# diving with the total amount of games\n", "# Produce venn diagram of the values\n", "\n", "count_a = 2055\n", "count_b = 1096\n", "count_c = 564\n", "\n", "count_ab = 1770\n", "count_ac = 583\n", "count_bc = 188\n", "\n", "count_abc = 522\n", "\n", "p_a = round(2055 / num_games, 3)\n", "p_b = round(1096 / num_games, 3)\n", "p_c = round(564 / num_games, 3)\n", "\n", "p_ab = round(1770 / num_games, 3)\n", "p_ac = round(583 / num_games, 3)\n", "p_bc = round(188 / num_games, 3)\n", "\n", "p_abc = round(522 / num_games, 3)\n", "\n", "plt.figure(figsize=(10, 5))\n", "venn = venn3(subsets=(p_a, p_b, p_ab, p_c, p_ac, p_bc, p_abc), set_labels=('A', 'B', 'C'))\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Probability: Blue Team does not manage to do any of the events (Outer White Section)" ] }, { "cell_type": "code", "execution_count": 287, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Probabilty that Blue Team loses, doesn't kill dragons and heralds: 0.3138981678307521\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Calculate the total amount of the games in the venn diagram\n", "# Find the complement of (A ∪ B ∪ C)\n", "\n", "count_all = count_a + count_b + count_c + count_ab + count_abc + count_ac + count_bc\n", "did_not_win_all = num_games - count_all\n", "prob_did_not_win_all = did_not_win_all / num_games\n", "\n", "print(\"Probabilty that Blue Team loses, doesn't kill dragons and heralds:\", prob_did_not_win_all)\n", "\n", "plt.figure(figsize=(10, 5))\n", "venn = venn3(subsets=(p_a, p_b, p_ab, p_c, p_ac, p_bc, p_abc), set_labels=('A', 'B', 'C'))\n", "\n", "plt.text(0.5, -0.5, f'{round(prob_did_not_win_all, 3)}', ha='center', va='center')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Probability: Blue Team wins and kills dragon and herald" ] }, { "cell_type": "code", "execution_count": 288, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Probability that blue team wins, kills dragon and herald: 0.053\n" ] } ], "source": [ "# The probability of this event is essentially the intersection of\n", "# A (Blue Team Wins), B (Kills Dragon) and C (Kills Herald)\n", "\n", "print(\"Probability that blue team wins, kills dragon and herald:\", p_abc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Probability: Blue Team does not win but kills dragon and the herald " ] }, { "cell_type": "code", "execution_count": 289, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Probability that blue team does not win but kills dragon and the herald : 0.019\n" ] } ], "source": [ "# Same with above but only with the intersection between\n", "# B (Kills Dragon) and C (Kills Herald)\n", "\n", "print(\"Probability that blue team does not win but kills dragon and the herald :\", p_bc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Probability: Blue Team wins but does not kill dragon and herald. " ] }, { "cell_type": "code", "execution_count": 290, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Probability that blue team wins without killing the dragon and the herald: 0.208\n" ] } ], "source": [ "# Same with above but only with the A section (Blue Team wins)\n", "\n", "print(\"Probability that blue team wins without killing the dragon and the herald:\", p_a)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.12.6" } }, "nbformat": 4, "nbformat_minor": 4 }