Question

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards, then the mean of the number of queens is

• A. $\frac{2}{23}$
• B. $\frac{2}{13}$
• C. $\frac{1}{13}$
• D. $\frac{3}{13}$

Answer 1

The correct option is B $\frac{2}{13}$

The number of queens is a random variable.
Let it be denoted by $X$. Clearly, $X$ can take the values $0,1,\text{or}2$

$X$	$0$	$1$	$2$
$P\left(X\right)$	$\frac{144}{169}$	$\frac{24}{169}$	$\frac{1}{169}$

$\mu =\sum XP\left(X\right)=\frac{2}{13}$