Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If $μ$ and $σ^{2}$ represent mean and variance of X, respectively, then $10 (μ^{2} + σ^{2})$ is equal to

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answer is B.

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Detailed Solution

Mean
$\begin{array}{r} (μ) = \sum X_{i} P_{i} \\ = 0 \times \frac{1}{6} + 1 \times \frac{1}{2} + 2 \times \frac{3}{10} + 3 \times \frac{1}{30} = \frac{6}{5} \end{array}$
Variance $(σ^{2}) = \sum X_{i}^{2} P_{i} - μ^{2}$
$= 0 \times \frac{1}{6} + 1 \times \frac{1}{2} + 4 \times \frac{3}{10} + 9 \times \frac{1}{30} - \frac{36}{25} = \frac{14}{25}$
So, $10 (μ^{2} + σ^{2}) = 10 (\frac{36}{25} + \frac{14}{25}) = 20$