probability question

Question

1.The Toronto Maple Leafs are

facing the Montréal Canadiens in a best

of seven playoff series. The first team to

win four games wins the series. Ties are

broken through sudden decision overtime.

Assuming that the teams are evenly

matched,

a) what are the odds in favour of either

team sweeping the series, in which one

team wins four consecutive games?

b) what are the odds against the series going

a full seven games?

Answer 1

1. Probability Toronto sweeps = (0.5)^4 + Probability Montreal sweeps = 0.5^4 = 0.0625 * 2 = 0.125 =1/8

odds = 1/8 / 1-1/8) = 1/7 or 1:7

1. Use negative binomial distribution:

Probability Toronto wins 4th game in 7 tries = C(6,3) (0.5)^7 = 0.3125 +

same for Montreal (0.3125) = 0.625 = 5/8

odds = (5/8)/(1-5/8) = 5/3 = 5:3