Events A and B are independent. The probability that both events A and B occur is 0.15. Additionally, the probability that event A occurs while event B does not occur is 0.45. What is the probability that at least one of the events A and B occurs?

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0.55

0.7

Correct

0.75

0.8

0.85

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Official Explanation

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To find the probability that at least one of the events A and B occurs, we can use the formula: Probability that Event A occurs and B does not occur + Probability that Event B occurs and A does not occur + Probability that both events A and B occur. This can be expressed as: A*(1-B) + B*(1-A) + A*B. Given that the probability that both events A and B occur is 0.15 (i.e., A*B = 0.15) and the probability that event A occurs while event B does not occur is 0.45 (i.e., A*(1-B) = 0.45), we can solve for A and B. From A*(1-B) = 0.45, we have A - AB = 0.45. Substituting AB = 0.15 into this…

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What this question tests

What it tests

Your ability to compute probabilities of single and compound events, including 'at least one' questions.

Common trap

Forgetting to use the complement for 'at least one', or treating dependent events as independent.