A high school senior applies for admission to college A and to college B. He estimates that the probability of his being rejected by B is 0.5, that his application will be accepted at A with a probability of 0.3, and that the probability of at least one of his applications being rejected is 0.9. What is the probability that:

a) he will be accepted by both colleges?

b) he will be rejected by exactly one college?

c) he will be accepted by B and rejected by A?

d) given that he has been accepted by A, he will be accepted by B?