Question

Two cards are drawn simultaneously from a well shuffled pack of $52$ cards. The expected number of aces is

• A. $\frac{4}{13}$
• B. $\frac{3}{13}$
• C. $\frac{2}{13}$
• D. $\frac{1}{13}$

Answer 1

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

$P(X=0)=\frac{48C_2}{52C_2}P(X=1)=\frac{4C_1\ast 48C_1}{52C_2}P(X=2)=\frac{4C_2}{52C_2}E\left(X\right)={\sum }_0^2{x}_i{p}_i=\frac{48C_2}{52C_2}\ast 0+\frac{4C_1\ast 48C_1}{52C_2}\ast 1+\frac{4C_2}{52C_2}=\frac{204}{26\ast 51}=\frac{2}{13}$