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he Boomtown Bears are playing against the Tipton Toros in a baseball tournament. The winner of the tournament is the first team that wins three games. The Bears have a probability of \(\frac{2}{3}\) of winning each game. Find the probability that the Bears win the tournament.

 Apr 18, 2020
 #1
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We must consider strings like BBB and BBTB.  Going through the cases, we get a probability of (2/3)^3 + 3*(2/3)^3*(1/3)^2 + 6*(2/3)^3*(1/3)^4 = 304/729.

 Apr 18, 2020
 #2
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The Guest just mis-typed the final result:  (2/3)3  +  3·(2/3)3·(1/3)  +  6·(2/3)3·(1/3)2  =  64/81

 

Winning in three games:   BBB

Winning in four games:     BBTB, BTBB, TBBB

Winning in five games:     BBTTB, BTTBB, BTBTB, TBBTB, TBTBB, TTBBB

 Apr 19, 2020
 #3
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This problem has stomped me for sooooo long. Now thanks to your help, I learned how to do problems like this!

 Apr 19, 2020

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