A class committee of 3 is chosen at random from 5 boys and 4 girls. What is the probability that the committee has exactly 2 girls?

\frac{5}{14}

Correct answerYour answer

\frac{1}{21}

Correct answerYour answer

\frac{17}{42}

Correct answerYour answer

\frac{4}{9}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

All committees: ${}^{9}C_{3} = 84$ .
Exactly 2 girls: ${}^{4}C_{2} \times {}^{5}C_{1} = 6 \times 5 = 30$ .
Probability $= \frac{30}{84} = \frac{5}{14}$ .

Worth noting

$\frac{17}{42}$ adds the all-girl committees (4 of them), which answers 'at least 2 girls'. $\frac{1}{21}$ is the chance of 3 girls, and $\frac{4}{9}$ is only the chance that one chosen person is a girl.

Concept: Probability of a selection using combinations
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsBasic probability

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Ten questions from Counting and Basic Probability, at your own pace.

A class committee of 3 is chosen at random from 5 boys and 4 girls. What is the probability that the committee has exactly 2 girls?

Explanation