AP Stats help? Free Response question (2 parts)

Question

On the Centerville High School debate team, 20% of the members are Sophomores, 35% are Juniors and 45% are Seniors. A team member is selected randomly to give the closing argument for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. If a junior gives the closing argument , the probability is 0.6 . If a senior closes, the probability rises to 0.85 .

(a) Find the probability that the teams wins the debate.

(b) Given that the team loses the debate, what is the probability that it was a junior who gave the closing argument ?

Answer 1

the sum of Pai P(B|Ai) = P(B)

.2(.25)+ .35(.6)+.45(.85) = .6425

.35(1-.6)/(1 - .6425) = .3916 or 56/143