9. The Stanley Cup winner is determined in the final series between two teams. T

Question

9. The Stanley Cup winner is determined in the final series between two teams. The first team to win 4 games wins the Cup. Suppose that Dallas Stars advance to the final series, and they have a probability of 0.55 to win each game, and the game results are independent of each other. Find the probability that a) Dallas Stars wins the Stanley Cup b) Seven games are required to determine the Cup winner (Hint: Without loss of generality, you can assume that the series continues until 7 games are played, even if the Cup winner is determined earlier. This "change of Stanley Cup rules" will not change the answer to the problem!)

Explanation / Answer

Probability of Dallas star winning = P( Win 4) +P( 5)+P(6)+P(7) = 7C4 * 0.55^4*0.45^3 + 7C5 * 0.55^5*0.45^2+7C6 * 0.55^6*0.45^1+7C7 * 0.55^7*0.45^0= 35 * 0.55^4*0.45^3 + 21* 0.55^5*0.45^2+7* 0.55^6*0.45^1+1* 0.55^7*0.45^0= 0.6082

P( Seven games are required ) = P( Dallas wins 3 of first 6)* P( other team winds 3 of first 6) = 6C3 * 0.55^3*0.45^3 = 20*0.55^3*0.45^3 = 0.3032

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