if an experiment has mutually exclusive outcomes . . .which of the following must be true?

Question

An experiment has three mutually exclusive outcomes, A, B, and C. If P (A) = 0.12, P (B) = 0.61, and P(C) = 0.27, which of the following must be true?
I. A and C are independent
II. P(A and B) =0
III. P(B or C) = P(B) + P(C)

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I ,II ,and III only

Answer 1

Hi Callie!

 

The answer is D. If events are mutually exclusive, then they do have no chance of occurring at the same time; thus, statement II is true. Similarly, if two events are mutually exclusive, then their union probability is simply the sum of their probabilities...there is  nothing to be subtracted out. Hence, statement III is true.

 

However, the first statement is not true. This is because, mutually exclusive events must be dependent. Events that are independent cannot be mutually exclusive. Therefore, mutually exclusive implies dependence and independence implies not mutually exclusive, but no other simple implications among these conditions hold true. 

 

I hope it helps

A