Two dice are thrown. Given that the product of the two numbers is even, what is the probability that their sum is even?

\frac{1}{3}

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\frac{1}{2}

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\frac{2}{3}

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\frac{3}{4}

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CorrectNot quiteAnswer A

Correct answer: A

The product is odd only when both numbers are odd, in 9 outcomes, so it is even in $36 - 9 = 27$ .
An even product with an even sum needs both numbers even: 9 outcomes, so $\frac{9}{27} = \frac{1}{3}$ .

Worth noting

$\frac{1}{2}$ is the chance of an even sum with no condition; an even product rules out the 9 odd–odd outcomes, and all of them have even sums.

Ten questions from Conditional Probability & Bayes' Theorem, at your own pace.

Explanation