Question

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. The variance of the number of aces is

• A. $24/169$
• B. $\sqrt{24/169}$
• C. $\sqrt{24/173}$
• D. $24/173$

Answer 1

Answer: (A)

$24/169$

Let $X$ denote the number of aces $X$ can tare values of $0,1,2$
Let $S$ be the sample space
$\Rightarrow n\left(S\right)=52$
Let $E$ be the event of getting an ace probability of getting an ace $\left(p\right)$
$=\frac{n\left(E\right)}{n\left(S\right)}=\frac{4}{52}=\frac{1}{13}$
Probability of not getting an ace $\left(q\right)=1-p$
$=1-\frac{1}{13}=\frac{12}{13}$
we know that $n=2$
Mean $=np=2\left(\frac{1}{13}\right)=\frac{2}{13}$
variance $=npq=2\left(\frac{1}{13}\right)\left(\frac{12}{13}\right)=\frac{24}{169}$