Question

If a and b are mutually exclusive events with P(a) = 0.70, then P(b):

A) P(b) = 0.70
B) P(b) = 0.30
C) P(b) = 1.00
D) P(b) = 0.50

Answer 1

The probability of event b, given that a and b are mutually exclusive and P(a) = 0.70, is P(b) = 0.30. This is because the sum of the probabilities of mutually exclusive events must equal 1.

Step-by-step explanation:

If a and b are mutually exclusive events with P(a) = 0.70, then the next step is to understand that since they are mutually exclusive, they cannot occur at the same time, which means that P(a AND b) is 0. Knowing this, the sum of the probabilities of mutually exclusive events is equal to the probability of either event occurring, which gives us P(a OR b) = P(a) + P(b). Since in a total probability model, the sum of all possible outcomes is 1, we get P(a) + P(b) = 1. Therefore, if P(a) = 0.70, to find P(b) we rearrange the equation to P(b) = 1 - P(a), which gives us P(b) = 1 - 0.70 = 0.30.

So, the answer to the question is B) P(b) = 0.30.