{ "metadata": { "name": "", "signature": "sha256:df5d01aa3d313a1ff9125d050f7579444f637a48655659849348eb8e70633db4" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "from scipy.misc import factorial,comb\n", "factorial(10)/(factorial(6)*factorial(4)),comb(10,4,exact=True)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 1, "text": [ "(210.0, 210)" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "While the above functions could be used, recall that `arange(365,365-70,-1)` gives an array of the seventy numbers from 365 down to 296,\n", "so `arange(365,365-70,-1)/365.` gives an array of the successive fractions of not having a coincident birthday, and `1-cumprod(arange(365,365-70,-1)/365.)` then gives the probability of at least one coincidence for numbers of people from 1 through 70.
\n", "Similarly, `ones(69)/365.` is an array of 69 copies of 1/365. so `cumprod(ones(69)*364./365.)` gives successive powers of `1/365.`, and 1 minus that gives the probability of coincidence with a given specific person for numbers of people from 2 through 70.\n", "These two functions can be plotted as follows:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(range(1,71),1-cumprod(arange(365,365-70,-1)/365.),'r+')\n", "plot(range(2,71),1-cumprod(ones(69)*364./365.),'g+');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAEACAYAAABMEua6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMdQlqUUMdUlqEUNdklrEUJekFvl/or6movhKZdkAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can make the graph a bit larger, and add a grid, to see that the probability of coincident birthdays exceeds .5 starting at `n` equal to 23, is about .97 at `n` equal to 50, and is virtually guaranteed by `n` equal to 70:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "figure(figsize=(8,6))\n", "plot(range(1,71),1-cumprod(arange(365,295,-1)/365.),'r+')\n", "plot(range(2,71),1-cumprod(ones(69)*364./365.),'g+')\n", "yticks(arange(0,1.1,.1));\n", "xlim(0,70)\n", "xticks(range(0,71,5))\n", "grid('on')\n", "legend([r'$1-\\frac{365!}{(365-n)!\\ 365^n}$',\n", " r'$1-(\\frac{364}{365})^{n-1}$'],\n", " numpoints=3,loc='upper left',fontsize=18);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAeUAAAFwCAYAAACGm2OSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also expand the range to see what happens to the second curve when we reach `n` equal to 365, by plotting\n", "\n", " plot(range(1,366),1-cumprod(arange(365,0,-1)/365.),'r')\n", " plot(range(2,366),1-cumprod(ones(364)*364./365.),'g')\n", "\n", "Or we can define a function, and use `subplot` to put the two figures side by side.\n", "At `n` equal to 365, the lower curve has a probability of roughly .63:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def bdayplot(n,inc=25,sym='',loc=None,):\n", " plot(range(1,n+1),1-cumprod(arange(365,365-n,-1)/365.),'r'+sym)\n", " plot(range(2,n+1),1-cumprod(ones(n-1)*364./365.),'g'+sym)\n", " xticks(range(0,n+1,inc))\n", " yticks(arange(0,1.1,.1))\n", " xlim(0,n)\n", " grid('on')\n", " legend([r'$1-\\frac{365!}{(365-n)!\\ 365^n}$',\n", " r'$1-(\\frac{364}{365})^{n-1}$'],\n", " numpoints=3,loc=loc,fontsize=17);\n", " \n", "figure(figsize=(16,6))\n", "subplot(1,2,1)\n", "bdayplot(70,5,'+','upper left')\n", "subplot(1,2,2)\n", "bdayplot(365)\n", "plot([70,70],[0,1],c='gray',linestyle='--');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAA50AAAFwCAYAAAA7aR8/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that $\\frac{n(n-1)}{2}\\frac{1}{365}$ is a good approximation to the first function (red) for small $n$ (it just counts the number of pairs times the probability that a pair has coincident birthdays, so works as long as the pairs are approximately independent). \n", "Note also that $1-{\\rm e}^{-(n-1)/365}$ is a good approximation to the second function (green) for all $n$, hence the value $1-{\\rm e}^{-1}\\approx.63$ for $n=366$ in the above plot." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figure(figsize=(8,6))\n", "plot(range(1,71),1-cumprod(arange(365,365-70,-1)/365.),'r+')\n", "plot(range(2,71),1-cumprod(ones(69)*364./365.),'g+')\n", "xlim(0,70)\n", "ylim(0,1)\n", "grid('on')\n", "plot([n*(n-1)/(2.*365) for n in range(16)],'b')\n", "plot([1-exp(-(n-1)/365.) for n in range(366)],'y')\n", "xticks(range(0,75,5))\n", "yticks(arange(0,1.1,.1));\n", "legend([r'$1-\\frac{365!}{(365-n)!\\ 365^n}$',\n", " r'$1-(\\frac{364}{365})^{n-1}$',\n", " r'$\\frac{n(n-1)}{2}\\frac{1}{365}$',\n", " r'$1-{\\rm e}^{-(n-1)/365}$'],\n", " numpoints=3,loc='upper left',fontsize=14);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAeUAAAFwCAYAAACGm2OSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDnGBYb0ueJUAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }