City Scholarship Practice Exam

If A and B are independent with P(A) = 0.6 and P(B) = 0.5, what is P(A or B)?

0.6 0.8 0.3 0.5

Correct Answer:

0.8

Explanation:

Think about the chance that at least one of A or B occurs. For any two events, P(A or B) = P(A) + P(B) − P(A and B). Since A and B are independent, the probability both occur is P(A and B) = P(A)P(B) = 0.6 × 0.5 = 0.3. Plugging in gives P(A or B) = 0.6 + 0.5 − 0.3 = 0.8. So the probability that at least one of A or B happens is 0.8. This uses the idea that you add the probabilities of each event but subtract the overlap because it’s counted twice, and for independent events that overlap equals the product.

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