# The events A and B are mutually exclusive. Suppose P(A)=0.28 and P(B)=0.43 a.What is the...

## Question:

The events A and B are mutually exclusive. Suppose P(A)=0.28 and P(B)=0.43

a.What is the probability of either A or B occuring? (Round your answer to 2 decimal places.)

b. What is the probability that neither A nor B will happen? (Round your answer to 2 decimal places.)

## Mutually Exclusive Events

The events are considered mutually exclusive if they cannot occur at the same time. For example, it might rain or be sunny at any given time, but it cannot be both. If the sum of mutually exclusive events is 1, they are called collectively exhaustive.

a. The probability of either of mutually exclusive events occurring is the sum of their probabilities, i.e.,

{eq}P(A \cup B) = P(A)+P(B) = 0.28+0.43 = 0.71 {/eq}

b. The probability that neither of mutually exclusive event occurs is the complementary event to the event of either of them occurring, i.e.,

{eq}P(\neg A \cap \neg B)=1-P(A \cup B)=1-0.71 = 0.29 {/eq} 