If events A and B are disjoint with P(A) = 0.25 and P(B) = 0.40, what is P(A ∪ B)?

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Multiple Choice

If events A and B are disjoint with P(A) = 0.25 and P(B) = 0.40, what is P(A ∪ B)?

Explanation:
Disjoint events cannot happen at the same time, so the probability of either one occurring is the sum of their probabilities. Here, P(A ∪ B) = P(A) + P(B) = 0.25 + 0.40 = 0.65. Since there is no overlap, you don’t subtract any overlap term (P(A ∩ B) = 0). In general, P(A ∪ B) = P(A) + P(B) − P(A ∩ B); the disjoint condition makes the intersection term zero, leaving just the sum.

Disjoint events cannot happen at the same time, so the probability of either one occurring is the sum of their probabilities. Here, P(A ∪ B) = P(A) + P(B) = 0.25 + 0.40 = 0.65. Since there is no overlap, you don’t subtract any overlap term (P(A ∩ B) = 0). In general, P(A ∪ B) = P(A) + P(B) − P(A ∩ B); the disjoint condition makes the intersection term zero, leaving just the sum.

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