More GRE studying, here was a practice question I was confused on, and the last of the probability ones:
Let A, B, C, and D be events for which and P(A or B) = 0.6, P(A) = 0.2, P(C or D) = 0.6, and P(C) = 0.5. The events A and B are mutually exclusive, and the events C and D are independent.
(a) Find P(B)
This was is easy. P(B) = P(A or B) – P(A) = .4
(b) Find P(D)
I don't understand why I can't use the same logic for this answer. There is likely something fundamentally wrong with my distinction between mutually exclusive events and independent events. Why is the answer .2?