If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?
A) 0.
B) 0.50
C) 1.00
D) cannot be determined from the information given

Question

Quizplus · Accepted Answer

If the events A and B are mutually exclusive, this means they cannot occur simultaneously. Therefore, the sum of their probabilities is 1. If they are also collectively exhaustive, this means that they represent all possible outcomes of an experiment. Since they are equally likely, they must have the same probability of occurrence, let's call it P(A) = P(B). Then, P(A) + P(B) = 1 implies that 2P(A) = 1, and thus P(A)= 0.5 or 50%. Therefore, the probability that event A occurs is 0.50 or choice B.

If Two Equally Likely Events a and B Are Mutually