With P(A) = 0.3, P(B) = 0.6, and P(A ∩ B) = 0.2, what is P(A ∪ B)?

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Multiple Choice

With P(A) = 0.3, P(B) = 0.6, and P(A ∩ B) = 0.2, what is P(A ∪ B)?

Explanation:
When two events can happen, the probability that at least one occurs is found using inclusion-exclusion: P(A ∪ B) = P(A) + P(B) − P(A ∩ B). Here that becomes 0.3 + 0.6 − 0.2 = 0.7. The idea is that adding P(A) and P(B) counts the overlap area twice, so you subtract the intersection once to count each outcome only once. This yields a feasible probability of 0.7. If A and B had no overlap, the union would be 0.9; the overlap of 0.2 reduces it to 0.7.

When two events can happen, the probability that at least one occurs is found using inclusion-exclusion: P(A ∪ B) = P(A) + P(B) − P(A ∩ B). Here that becomes 0.3 + 0.6 − 0.2 = 0.7. The idea is that adding P(A) and P(B) counts the overlap area twice, so you subtract the intersection once to count each outcome only once. This yields a feasible probability of 0.7. If A and B had no overlap, the union would be 0.9; the overlap of 0.2 reduces it to 0.7.

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