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???

Answer 1

To sweep the series a team must have won 4 straight games.
Since the prob of a win is 1/2
the prob of sweep = (1/2)^4 = 1/16
then prob of NOT sweeping the series = 15/16
odds in favor of a sweep = 1 : 15

To go the full 7 games, the outcomes must be WWWWLLL
For the winning team that prob is C(7,4)(1/2)^4 (1/2)^3 = 35/128
consequently the prob of NOT going the 7 games = 93/128

So the odds in favor of not going the full 7 games = 93 : 35

Answer 2

Seems like mathhelper gave you a wrong solution. Math helper. WWWWLLL is not possible since WWWW is the end of game. WWWLLLW is the starting point. you can't just go by four same letters since that means the games over. there are 20 possibilities out of 128 since its (1/2)^7 for each, so odds in favor of not going the full 7 games= 11:5