If E and F are independent with P(E)=0.6 and P(F)=0.5, what is P(E ∨ F)?

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Multiple Choice

If E and F are independent with P(E)=0.6 and P(F)=0.5, what is P(E ∨ F)?

Explanation:
This question tests how to combine probabilities for two independent events to get the chance that at least one occurs. For independent events, the probability of both happening is the product P(E)P(F). The probability that at least one occurs is the union, given by P(E ∪ F) = P(E) + P(F) − P(E)P(F). Here, P(E)P(F) = 0.6 × 0.5 = 0.3. So P(E ∪ F) = 0.6 + 0.5 − 0.3 = 0.8. You can also see this by the complement: neither occurs has probability (1−0.6)(1−0.5) = 0.4×0.5 = 0.2, so at least one occurs is 1 − 0.2 = 0.8.

This question tests how to combine probabilities for two independent events to get the chance that at least one occurs. For independent events, the probability of both happening is the product P(E)P(F). The probability that at least one occurs is the union, given by P(E ∪ F) = P(E) + P(F) − P(E)P(F).

Here, P(E)P(F) = 0.6 × 0.5 = 0.3. So P(E ∪ F) = 0.6 + 0.5 − 0.3 = 0.8. You can also see this by the complement: neither occurs has probability (1−0.6)(1−0.5) = 0.4×0.5 = 0.2, so at least one occurs is 1 − 0.2 = 0.8.

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