If A and B are mutually exclusive events with P(A) = 0.4 and P(B) = 0.5, what is P(A or B)?

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Multiple Choice

If A and B are mutually exclusive events with P(A) = 0.4 and P(B) = 0.5, what is P(A or B)?

Explanation:
When two events cannot happen at the same time, the chance that either one occurs is the sum of their individual chances. The general rule is P(A ∪ B) = P(A) + P(B) − P(A ∩ B). Since A and B are mutually exclusive, P(A ∩ B) = 0, so P(A ∪ B) = 0.4 + 0.5 = 0.9. This value makes sense because probabilities add up to at most 1, and here they do. If you only counted one event you’d get 0.4 or 0.5, and if you thought neither occurs you’d get 0.0, but the correct total for either event is 0.9.

When two events cannot happen at the same time, the chance that either one occurs is the sum of their individual chances. The general rule is P(A ∪ B) = P(A) + P(B) − P(A ∩ B). Since A and B are mutually exclusive, P(A ∩ B) = 0, so P(A ∪ B) = 0.4 + 0.5 = 0.9. This value makes sense because probabilities add up to at most 1, and here they do. If you only counted one event you’d get 0.4 or 0.5, and if you thought neither occurs you’d get 0.0, but the correct total for either event is 0.9.

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