Question

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 $\mu$ and ${\sigma }^2$ represent mean and variance of $X$, respectively, then $10\left({\mu }^2+{\sigma }^2\right)$ is equal to

• A. 250
• B. 20
• C. 25
• D. 30

Answer 1

Answer: (B)

$X$	$P(X)$	$XP(X)$	$X^{2}P(X)$
0	1/6	0	0
1	1/2	1/2	1/2
2	3/10	6/10	12/10
4	1/30	1/10	9/30

$\sum xP(x)=\frac{6}{2}=\mu$
${\sigma }^2=\sum x^{2}P(x)-{\mu }^2$
${\sigma }^2+{\mu }^2=0+\frac{1}{2}+\frac{12}{10}+\frac{9}{30}=2$
$10\left({\sigma }^2+{\mu }^2\right)=20\text{ Ans. }$