Nice try Mmm but you forgot some of the posibilities

The 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 1/5 of winning each game. Find the probability that the Bears win the tournament.

**I will assume that it is imposible to draw.**

P(B wins) = 1/5

P(B wines 3 games out of 3) = 1/ 5^3 = 25 / 5^5

P(B wins 3 games out of 4) = 4C3 * (1/5)^3 * (4/5) = 4 * 4 / 5^4 = 16 / 5^4 = 80 / 5^5

P ( B wins 3 games out of 5) = 5C3 * (1/5)^3 *( 4/5)^2 = 10 * 16 / 5^5 = 160 / 5^5

add them together 25+80+160 = 265

265 / 5^5 simplifies to 53/625 = 0.0848

So the prob that the bears win is 8.48%