def playseries(numgamesteamprob)"""assumes numgames an odd integerteamprob float between and returns true if better team wins series""numwon for game in range(numgames)if random random(<teamprobnumwon + return (numwon numgames// def simseries(numseries)prob fracwon [probs [while prob < serieswon for in range(numseries)if playseries( prob)serieswon + fracwon append(serieswon/numseriesprobs append(probprob + pylab plot(probsfracwonlinewidth pylab xlabel('probability of winning game'pylab ylabel('probability of winning series'pylab axhline( pylab ylim( pylab title(str(numseriesseven-game series'simseries( figure world series simulation when simseries is used to simulate seven-game seriesit produces the plot on the right notice that for the better team to win of the time ( on the -axis)it needs to be more than three times better than its opponent that is to saythe better team needs to winon averagemore than three out of four games ( on the -axisfor comparisonin the two teams in the world series had regular season winning percentages of (new york yankeesand (philadelphia philliesthis suggests that new york should win about of the games between the two teams our plot tells us that even if they were to play each other in seven-game seriesthe yankees would win less than of the time suppose we assume that these winning percentages are accurate reflections of the relative strengths of these two teams how many games long should the