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:

Question

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..

Answer 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.

against:
same as 1-prob that it is cleared in six games
how to go six games
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the probability of those events added together is
2(1/2)^6*10=20/64=10/32

now prob of being cleared in five games
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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