Created
June 5, 2018 08:40
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The Birthday Problem
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## The Birthday Problem\n", | |
"\n", | |
"#### Formal question:\n", | |
"\n", | |
"If you have $n$ students in your classroom. What is the probability that at least two of them share the same birthday?" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 92, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import math\n", | |
"import matplotlib \n", | |
"from matplotlib import pyplot as plt\n", | |
"\n", | |
"%matplotlib inline" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 100, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"def rectill(x, y):\n", | |
" if y == 0:\n", | |
" return x\n", | |
" return x * rectill(x-1, y-1)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 101, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"dic = {}\n", | |
"\n", | |
"for i in range(2, 120):\n", | |
" dic[i] = 1 - (rectill(365, i-1) / math.pow(365,i))" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 102, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[<matplotlib.lines.Line2D at 0x18a4300a320>]" | |
] | |
}, | |
"execution_count": 102, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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DxqW+rqg6GgAA0EEKIQA67PYla/KhK27L3KVr89L9d8snX7lfdh3Up+pYAADAM6QQAuBp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\nSZIkSVLNWAhJkiRJkiTVzP8A37y0QJ4ZtDYAAAAASUVORK5CYII=\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x18a42f255c0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.figure(figsize=(20,8))\n", | |
"plt.plot(list(dic.keys()), list(dic.values()))" | |
] | |
} | |
], | |
"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": "3.6.1" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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