Which statement correctly describes mutual exclusivity between two events A and B?

Which statement correctly describes mutual exclusivity between two events A and B?

• A. The two events cannot occur together, so P(A ∩ B) = 0.
• B. P(A ∩ B) = P(A)P(B).
• C. P(A ∩ B) = P(A|B).
• D. P(A ∩ B) = P(B|A).

Answer: (A)

Mutually exclusive events cannot happen at the same time. That means the probability of both occurring—the intersection—must be zero, so P(A ∩ B) = 0. This is the defining feature: there is no overlap between A and B. The other statements describe different relationships. For example, independence would require P(A ∩ B) to equal P(A)P(B), which is not guaranteed by exclusivity and often isn’t zero. The conditional-probability forms, P(A ∩ B) = P(A|B) or P(A ∩ B) = P(B|A), don’t hold in general for mutually exclusive events unless trivial cases occur (like one event having probability zero).

Mutually exclusive events cannot happen at the same time. That means the probability of both occurring—the intersection—must be zero, so P(A ∩ B) = 0. This is the defining feature: there is no overlap between A and B.

The other statements describe different relationships. For example, independence would require P(A ∩ B) to equal P(A)P(B), which is not guaranteed by exclusivity and often isn’t zero. The conditional-probability forms, P(A ∩ B) = P(A|B) or P(A ∩ B) = P(B|A), don’t hold in general for mutually exclusive events unless trivial cases occur (like one event having probability zero).