3-15. Suppose A and B are events within the sample space S and that P(A) =

P(B) = 1 2 .

Answer the following:

(a) If P(B|A) = 1 2 , are A and B independent? Are A and B mutually exclusive?

(b) If A and B are independent, what is the probability that “A occurs and B does not occur or B occurs and A does not occur”?

(c) If event C ⊂ S and P(C

A ∩ B) = 1 2 , find P(A ∩ B ∩ C).

(d) If A and B are independent and P(B|A) = 1 2 , find P(A ∪ B).