SOLUTION: two teams, And B,play a series of games of team A has probability .4 of winning each game,is it to its advantage to play the best of three out of five games or the best four out of

Question 367165: two teams, And B,play a series of games of team A has probability .4 of winning each game,is it to its advantage to play the best of three out of five games or the best four out of seven? Assume the outcomes of successive games are independent.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
It is to A's advantage to play as short a series as possible because the probability of winning each game is below 50%
in a 3 game series.
.4^2=.16 win....1st 2 games....lose .6^2=.36
.
1-(.16+.36)=.48
.
.4*.48=.192....win 2 out of 3.....lose .6*.48=.288
.
.16+.192=.352 chance of winning a 3 game series
As you can see the chance of winning a 3 game series is less than the chance of the team winning a single game and it gets worse the longer the series played.
.
Ed

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