366 lines
62 KiB
Plaintext
366 lines
62 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# MAT-204:00010 - Probability\n",
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"Author: Thanawin Pattanaphol - Date: 23th December 2024 - Description: Basic probability calculations"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Importing Libraries"
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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": 1,
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"metadata": {},
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"outputs": [
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{
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"ename": "ModuleNotFoundError",
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"evalue": "No module named 'pandas'",
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"output_type": "error",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)",
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"Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mpandas\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mpd\u001b[39;00m \n\u001b[1;32m 2\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_venn\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m venn3\n\u001b[1;32m 3\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pyplot \u001b[38;5;28;01mas\u001b[39;00m plt \n",
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"\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'pandas'"
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]
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}
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],
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"source": [
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"import pandas as pd \n",
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"from matplotlib_venn import venn3\n",
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"from matplotlib import pyplot as plt \n",
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"\n",
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"Dat = pd.read_csv('DataLoL.csv')\n",
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"\n",
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"num_games = len(Dat)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Questions"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"#### Probability: Blue Team wins"
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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": null,
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"metadata": {},
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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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"Probability that Blue Team wins is: 0.4990383642069035\n"
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]
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}
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],
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"source": [
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"# Calculating the probability by diving the amount of games that blue won\n",
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"# dividing it by the amount of total games\n",
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"# Thus: p = Number of time an event occurs / Total nmumber of possible events\n",
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"prob_blue_wins = len(Dat[Dat['blueWins'] == 1]) / num_games\n",
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"print(\"Probability that Blue Team wins:\", prob_blue_wins)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"#### Probability: Blue Team wins and kills the dragon"
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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": null,
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"metadata": {},
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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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"Probability that Blue Team wins and kills the dragon is: 0.23200728818706348\n"
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]
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}
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],
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"source": [
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"# Doing a similar calculation with the difference being\n",
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"# the number of time an event occurs now only counts\n",
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"# the number of times blue team wins and kills the dragon\n",
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"\n",
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"prob_blue_wins_dragons = len(Dat[(Dat['blueWins'] == 1) & (Dat['blueDragons'] == 1)]) / num_games\n",
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"print(\"Probability that Blue Team wins and kills the dragon:\", prob_blue_wins_dragons)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"#### Probability: Blue Team wins and kills the herald"
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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": null,
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"metadata": {},
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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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"Probability that Blue Team wins and kills the herald is: 0.11185342646016803\n"
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]
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}
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],
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"source": [
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"# Similar calculation but with the number of events that\n",
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"# team blue wins and kills the herald\n",
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"\n",
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"prob_blue_wins_heralds = len(Dat[(Dat['blueWins'] == 1) & (Dat['blueHeralds'] == 1)]) / num_games\n",
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"print(\"Probability that Blue Team wins and kills the herald:\", prob_blue_wins_heralds)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"#### Count: All possible cases (Venn Diagram)"
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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": null,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"# Declaring variable for each set\n",
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"# Loop through the whole games dataset and if the item-\n",
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"# -matches the condition, add it to the set for that\n",
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"# condition list\n",
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"\n",
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"game_blue_wins, game_blue_dragon, game_blue_herald = set()\n",
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"\n",
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"for game in range(num_games):\n",
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" if(Dat['blueWins'][game] == 1):\n",
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" game_blue_wins.add(game)\n",
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" if(Dat['blueDragons'][game] == 1):\n",
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" game_blue_dragon.add(game)\n",
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" if(Dat['blueHeralds'][game] == 1):\n",
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" game_blue_herald.add(game)\n",
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"\n",
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"venn3([game_blue_wins, game_blue_dragon, game_blue_herald], ('A', 'B', 'C'))\n",
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"\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"#### Probability: Each possible events (Venn Diagram)"
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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": null,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"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",
|
|||
|
|
"venn = venn3(subsets=(p_a, p_b, p_ab, p_c, p_ac, p_bc, p_abc), set_labels=('A', 'B', 'C'))"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"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": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"Probabilty that Blue Team loses, doesn't kill dragons and heralds: 0.3138981678307521\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"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 - p_all_wins\n",
|
|||
|
|
"\n",
|
|||
|
|
"print(\"Probabilty that Blue Team loses, doesn't kill dragons and heralds:\", did_not_win_all / num_games)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"#### Probability: Blue Team wins and kills dragon and herald"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"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": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"Probability that blue team kills dragon and the herald but does not win: 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": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"Probability that blue team wins without killing the graon 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": "3.12.3"
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
"nbformat": 4,
|
|||
|
|
"nbformat_minor": 2
|
|||
|
|
}
|