# Probability and independent vs mutually exclusive events

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?

• Independent means the two events don't affect each other in any way. Mutually exclusive means each event blocks the other. – anon Jul 29 '11 at 20:22

-"mutually exclusive events" means they are complements of each other, either A or B happens

-"independent events" means they are independent of each other

P(A or B) = P(A)+P(B) - P(A and B)

A and B are mutually exclusive events => P(A and B) = 0.

P(C or D) = P(C) + P(D) - P(C and D)

C and D are independent events => P(C and D) = P(C) * P(D)

=> 0.6 = 0.5 + P(D) - 0.5*P(D)

=> P(D) = 0.2

• "Mutually exclusive" doesn't mean that A and B are complements; there might be other events, e.g. C that also could occur if neither A nor B does. The statements in the 3rd and 4th lines are correct, but are consistent with this possibility. – Mars Aug 13 '13 at 16:23

If events are mutually exclusive, they are very dependent. The occurrence of one precludes that of another.

Because their properties are different:

For mutuall exclusive evnts P(A and B) = 0 For independent events P(A and B) = P(A)P(B)