Question

Suppose that A and B are mutually exclusive events for which P(A) = 0.3 and P(B) = 0.5. What is the probability that either event A or event B occurs?

Answer 1

For mutually exclusive events A and B, with P(A) = 0.3 and P(B) = 0.5, the probability that either event occurs, P(A OR B), is simply the sum of their individual probabilities, leading to P(A OR B) = 0.8 or 80%.

Step-by-step explanation:

The question involves calculating the probability of either event A or event B occurring when A and B are mutually exclusive events. Since they cannot occur at the same time, the probability of A and B occurring simultaneously is zero. Therefore, the probability that either event A or event B occurs is simply the sum of their individual probabilities.

To find P(A OR B) for mutually exclusive events, we use the formula:

P(A OR B) = P(A) + P(B) - P(A AND B)

Since P(A AND B) = 0 for mutually exclusive events:

P(A OR B) = P(A) + P(B)

Given that P(A) = 0.3 and P(B) = 0.5:

P(A OR B) = 0.3 + 0.5 = 0.8

Thus, the probability that either event A or event B occurs is 0.8, or 80%.