# The events A and B are mutually exclusive. Suppose P(A) = 30 and P(B)= 20. a. What is the...

## Question:

The events A and B are mutually exclusive. Suppose P(A) = 30 and P(B)= 20.

a. What is the probability of either A or B occurring?

b. what is the probability that neither A nor B will happen?

## Mutually Exclusive

When two events are mutually exclusive, it means that they cannot happen at the same time. Thus, the probability of both of them occurring together is zero. To find the probability that either could happen, we can add up the individual probabilities of the events.

First, since the probability of an event must be less than 1, we need to assume that these are percentages. This means that P(A) = 0.3 and P(B) = 0.2.

a. Since these are mutually exclusive events, there is no overlap between them. Thus, to find the probability that either A or B occurs, we can add up the individual probabilities of A and B occurring.

{eq}P(A \cup B) = 0.2 + 0.3 = 0.5 {/eq}

b. To find the probability that neither A or B happens we can subtract the probability we just calculated from 1. This is because there are two cases: either A or B happens, or neither A or B happens. Every possible outcome is contained in those two cases.

{eq}P(A \cup B)^C = 1-0.5 = 0.5 {/eq}