Question

Suppose a and b are mutually exclusive events, and that
A) p(a)=0.22 and
B) p(b)=0.42.

Answer 1

In summary, events A and B are mutually exclusive with probabilities 0.22 and 0.42, respectively. Their combined probability, or P(A OR B), is 0.64, indicating the likelihood of either event A or B occurring.

Step-by-step explanation:

When we talk about mutually exclusive events, we refer to two events that cannot occur at the same time. For these events, the probability of both occurring simultaneously is zero, which is denoted as P(A AND B) = 0.

In the question, we're given that events A and B are mutually exclusive, with P(A) = 0.22 and P(B) = 0.42. Let's consider what these probabilities tell us about the outcome of these two events.

Since A and B cannot appear together, the probability of either A or B happening is the sum of their individual probabilities. Therefore, if we want to find P(A OR B), we can use the following formula:

• P(A OR B) = P(A) + P(B)

Plugging in the values, we get:

• P(A OR B) = 0.22 + 0.42 = 0.64

This tells us that the probability of either A or B occurring is 0.64.