If A and B are independent events with P(A) = 0.5 and P(B) = 0.4, what is P(A ∪ B)?

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Multiple Choice

If A and B are independent events with P(A) = 0.5 and P(B) = 0.4, what is P(A ∪ B)?

Explanation:
When two events are independent, the chance that at least one occurs uses the inclusion-exclusion idea: P(A ∪ B) = P(A) + P(B) − P(A)P(B). Here, P(A) = 0.5 and P(B) = 0.4, so the intersection is P(A)P(B) = 0.5 × 0.4 = 0.2. Plugging in gives P(A ∪ B) = 0.5 + 0.4 − 0.2 = 0.7. So, there is a 0.7 probability that either A or B (or both) occurs. If A and B weren’t independent, you’d need a different P(A ∩ B) value, and the calculation would change.

When two events are independent, the chance that at least one occurs uses the inclusion-exclusion idea: P(A ∪ B) = P(A) + P(B) − P(A)P(B). Here, P(A) = 0.5 and P(B) = 0.4, so the intersection is P(A)P(B) = 0.5 × 0.4 = 0.2. Plugging in gives P(A ∪ B) = 0.5 + 0.4 − 0.2 = 0.7. So, there is a 0.7 probability that either A or B (or both) occurs. If A and B weren’t independent, you’d need a different P(A ∩ B) value, and the calculation would change.

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