Question

Let A and B be two disjoint events such that P(A) = 0.32 and P(B) = 0.24. The probability that either event occurs P(A or B) is:

a) 0.56
b) 0.32
c) 0.24
d) 0.08

Answer 1

The probability that either event A or B occurs, given that they are disjoint events, is the sum of their probabilities, P(A) + P(B), which equals 0.56.

Step-by-step explanation:

The student's question involves finding the probability that either event A or event B occurs, given that A and B are two disjoint events with known probabilities P(A) = 0.32 and P(B) = 0.24. To solve the problem, we use the formula for the probability of the union of two disjoint (mutually exclusive) events, which is simply the sum of the probabilities of each event occurring separately. This is because if two events are disjoint, they cannot both happen at the same time - if one happens, the other cannot.

P(A or B) is equal to P(A) + P(B) since A and B are disjoint events. By adding the two probabilities together, we get:

P(A or B) = P(A) + P(B) = 0.32 + 0.24 = 0.56.

Therefore, the correct answer to the student's question is a) 0.56.