When selecting three integers from the first 12 positive integers, what is the likelihood that their product will be even?

Answer Choices

Correct answer marked below

\frac{9}{10}

\frac{3}{4}

\frac{7}{11}

\frac{11}{12}

\frac{10}{11}

Correct

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Explanation

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Official Explanation

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To find the probability that the product of three integers chosen from the first 12 positive integers is even, we first determine the total number of ways to choose 3 integers from 12, which is given by

\binom{12}{3} = 220

. Next, we calculate the number of ways to choose 3 integers such that their product is odd. This occurs only when all chosen integers are odd. The odd integers among…

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Comments

JahnviApr 6, 2025

Greatt

ZachariahMar 17, 2024

finally understood this

VNov 12, 2024

Thanks for sharingThank you for sharing!!thanks for sharing

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.