Which statement describes mutually exclusive outcomes?

Which statement describes mutually exclusive outcomes?

• A. The probabilities add to more than 1
• B. Both outcomes must occur together
• C. The outcome of one event cannot happen at the same time as the outcome of another
• D. The outcomes are independent of each other

Answer: (C)

Mutually exclusive outcomes are events that cannot both occur in the same trial. The statement describes this exactly: the outcome of one event cannot occur at the same time as the outcome of another. When one happens, the other is impossible, so they cannot happen together (P(A ∩ B) = 0). For context, if two events are mutually exclusive, knowing that one occurred means the other did not, which contrasts with independence where the occurrence of one event does not affect the probability of the other. An example is flipping a coin and getting heads or tails on a single flip—these outcomes cannot happen together. The other ideas—probabilities adding to more than 1, both outcomes occurring together, or outcomes being independent—describe different concepts and do not define mutual exclusivity.

Mutually exclusive outcomes are events that cannot both occur in the same trial. The statement describes this exactly: the outcome of one event cannot occur at the same time as the outcome of another. When one happens, the other is impossible, so they cannot happen together (P(A ∩ B) = 0).

For context, if two events are mutually exclusive, knowing that one occurred means the other did not, which contrasts with independence where the occurrence of one event does not affect the probability of the other. An example is flipping a coin and getting heads or tails on a single flip—these outcomes cannot happen together. The other ideas—probabilities adding to more than 1, both outcomes occurring together, or outcomes being independent—describe different concepts and do not define mutual exclusivity.