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.

awoafdwawda Apr 18, 2020

#1**0 **

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.

Guest Apr 18, 2020

#2**+1 **

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

geno3141 Apr 19, 2020

#3**0 **

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

awoafdwawda Apr 19, 2020