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In their upcoming best of seven (the first team to win 4 games, wins the series) NHL playoff series, the Toronto Maple Leafs have been given 5 : 3 odds in favour of winning any particular game. What is the chance they will win the best of 7 series against the Montreal Canadiens? (Remember, it could take more than 4 games to win the series!)

2 months ago

Answered By Majid B

P(W)=Probability that Toronto Maple Leafs wins each game

P(L)=Probability that Toronto Maple Leafs loses each game

P(W)/P(L)=5/3   ,  P(W)+P(L)=1    =>    P(W)/[1-P(W)]=5/3m    =>     P(W)=5/8  ,   P(L)=3/8 

We know that each team plays 6 times in the series.

A: Toronto Maple Leafs wins at least 4 games

P(A)=P(4W)+P(5W)+P(6W)

P(4W)=n(4W)*[P(W)^4]*[P(L)^2]=(6C4)*[(5/8)^4]*[(3/8)]^2]=0.322

P(5W)=n(5W)*[P(W)^5]*[P(L)]=(6C5)*[(5/8)^5]*(3/8)=0.215

P(6W)=n(6W)*[P(W)^6]=(6C6)*[(5/8)^6]=0.060

P(A)=0.322+0.215+0.060=0.597#60%