Two events A and B are disjoint with P(A)=0.4 and P(B)=0.5. What is P(A or B)?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

Two events A and B are disjoint with P(A)=0.4 and P(B)=0.5. What is P(A or B)?

Explanation:
Disjoint (mutually exclusive) events can’t happen at the same time, so the probability of either occurring is just the sum of their probabilities. Here, P(A) = 0.4 and P(B) = 0.5, so P(A or B) = 0.4 + 0.5 = 0.9. The overlap term is zero because they can’t both occur together. In general, P(A ∪ B) = P(A) + P(B) − P(A ∩ B); with disjoint events, P(A ∩ B) = 0, leaving the simple sum. So the result is 0.9.

Disjoint (mutually exclusive) events can’t happen at the same time, so the probability of either occurring is just the sum of their probabilities. Here, P(A) = 0.4 and P(B) = 0.5, so P(A or B) = 0.4 + 0.5 = 0.9. The overlap term is zero because they can’t both occur together. In general, P(A ∪ B) = P(A) + P(B) − P(A ∩ B); with disjoint events, P(A ∩ B) = 0, leaving the simple sum. So the result is 0.9.

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