The Bad News Bears are playing against the Houston Toros in a baseball tournament. The first team to win three games wins the tournament. The Bears have a probability of $\frac{2}{3}$ of winning each game. Find the probability that the Bears win the tournament.
-649 The Bears can win the tournament in three ways:
* They can win the first three games.
* They can lose the first game and then win the next two games.
* They can lose the first two games and then win the next three games.
The probability that the Bears win the first three games is (2/3)^3 = 8/27.
The probability that the Bears lose the first game and then win the next two games is (1/3)*(2/3)^2 = 2/27.
The probability that the Bears lose the first two games and then win the next three games is (1/3)^2*(2/3)^3 = 1/27.
So, the total probability that the Bears win the tournament is 8/27 + 2/27 + 1/27 = 11/27.
Therefore, the probability that the Bears win the tournament is 11/27.
