If two events A and B are independent with P(A)=1/2 and P(B)=1/3, what is P(A ∩ B)?

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Study for the Praxis 5165 Mathematics Test. Review with flashcards and multiple-choice questions, each with hints and explanations. Prepare effectively for success!

Multiple Choice

If two events A and B are independent with P(A)=1/2 and P(B)=1/3, what is P(A ∩ B)?

Explanation:
When two events are independent, the chance both happen is the product of their individual probabilities. So P(A ∩ B) = P(A) × P(B) = (1/2) × (1/3) = 1/6. This value, 1/6, is the correct result. The other numbers come from misapplying rules or thinking the events aren’t independent, but independence is precisely what lets you multiply the probabilities.

When two events are independent, the chance both happen is the product of their individual probabilities. So P(A ∩ B) = P(A) × P(B) = (1/2) × (1/3) = 1/6. This value, 1/6, is the correct result. The other numbers come from misapplying rules or thinking the events aren’t independent, but independence is precisely what lets you multiply the probabilities.

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