For mutually exclusive events, which statement is true?

For mutually exclusive events, which statement is true?

• A. They cannot occur at the same time
• B. They are always independent
• C. P(A ∪ B) = P(A) + P(B)
• D. P(A ∩ B) = P(A)P(B)

Answer: (A)

Mutually exclusive events are those that cannot happen on the same trial. This means their overlap is impossible, so P(A ∩ B) = 0. Because there’s no way for both to occur, the chance of either one happening is simply the sum of their individual probabilities. This situation does not imply independence; independence would require P(A ∩ B) = P(A)P(B), which is not generally true when the intersection is zero unless at least one of the probabilities is zero. So the direct statement—the two events cannot occur at the same time—best captures the concept.

Mutually exclusive events are those that cannot happen on the same trial. This means their overlap is impossible, so P(A ∩ B) = 0. Because there’s no way for both to occur, the chance of either one happening is simply the sum of their individual probabilities. This situation does not imply independence; independence would require P(A ∩ B) = P(A)P(B), which is not generally true when the intersection is zero unless at least one of the probabilities is zero. So the direct statement—the two events cannot occur at the same time—best captures the concept.