Question

11. A baseball team is known to win 75% of their games, and the team wins 90% of their home games. 50% of the teamís games are at home.

a. Given the team won their next game, what is the probability that it was a home game?

b. Given the team lost their next game, what is the probability it was a road game?

Answer 1

P(team win) = 75% = 0.75, P(team lost) = 1 - P(team win) = 1 - 0.75 = 0.25

P(team win | home game) = 90% = 0.90

P(Home games) = 50% = 0.50

P(Home game and team win) = P(team win | home games) * P(home games) = 0.90 * .50 = 0.45

P(Road games) = 1 - P(Home games) = 0.50

a. P(Home game | team win)

The probability that it was a home game given the team won their next game is 0.6

b. P(Road game | team lost)

P(Road game and the team lost) = P(team lost | road games) * P(road games) = 0.10*0.50 = 0.05