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

range of x = {0, 1, 2, 3}
The distribution is

x = x	0	1	2	3
P(x = x)	$\frac{^{7} c_{4}}{10 c_{4}} = \frac{1}{6}$	$\frac{^{3} c_{1} \times^{7} c_{3}}{10 c_{4}} = \frac{1}{2}$	$\frac{^{3} c_{2} \times^{7} c_{2}}{10 c_{4}} = \frac{3}{10}$	$\frac{^{3} c_{3} \times^{7} c_{1}}{10 c_{4}} = \frac{1}{30}$

$\begin{array}{l} σ^{2} + μ^{2} = \sum x^{2} P (x = x) \\ = 0 \cdot \frac{1}{6} + 1^{2} \cdot \frac{1}{2} + 2^{2} \cdot \frac{3}{10} + 3^{2} \cdot \frac{1}{30} \\ = \frac{20}{10} \\ ∴ 10 (σ^{2} + μ^{2}) = 20 \end{array}$