Two teams are playing in a best of seven playoff series. The first team to win four games wins the series. Ties are broken through sudden decision overtime. If the teams are evenly matched:
What are the odds in favour of either team sweeping the series, in which one team wins four consecutive games??? What are the odds against the series going a full seven games???

The answer says 1:7 for odds in favour, and 11:5 for against. I get 1:15 for the first, and I don't know how to get started on the second..

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  1. favor=Pr(w,w,w,w)=2(1/2)^4=1/8 which is 1:7

    notice the two in front, you asked for the pr of EITHER team.

    same as 1-prob that it is cleared in six games
    how to go six games
    the probability of those events added together is

    now prob of being cleared in five games
    pr of that is 2(1/2)^5*4=1/4

    pr cleared in four games is 1/8
    so proab against going seven games is sum of prob going 4,5,or 6 games

    10/32+1/8+1/4= 22/32=11/16 , so the probabiliity of going seven games is
    1-11/16=5/16 which is 11:5 odds

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