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?