Two teams, the Exponents and the Radicals, square off in a best of 5 math hockey tournament. Once a team wins 3 games, the tournament is over.

The schedule of the tournament (for home games) goes: E-R-E-R-E

If the Exponents are playing at home, there is a 60% chance they'll win. If they are playing on the road, there is a 45% chance they'll win.

Find the probability that the Exponents win the series. Find this probablitliy by using a tree diagram.

1 answer

hard to draw trees here, will do it in listing form

we want E to win, as soon as they win 2 games it is all over, no more than 3 games

Possible ways:
EE = .6^2 = .36
ERE = .6(.4)(.6) = .144
REE = .144

prob = sum of those = .648