Question

Two cards are drawn successively with replacement from a well-shuffled deck of $52$ cards. Let $X$ denote the random variable of number of aces obtained in the two drawn cards. Then $P(X=1)+P(X=2)$ equals

• A. $\frac{52}{169}$
• B. $\frac{25}{169}$
• C. $\frac{49}{169}$
• D. $\frac{24}{169}$

Answer 1

Answer: (B)

$\frac{25}{169}$

Two cards are drawn successively with replacement

$4Aces48$ Non Aces

$P(x=1)=\frac{{}^4{C}_1}{{}^{52}{C}_1}\times \frac{48C_1}{52C_1}+\frac{48C_1}{52C_1}\times \frac{4C_1}{52C_1}=\frac{24}{169}$

$P(x=2)=\frac{{}^4{C}_1}{{}^{52}{C}_1}\times \frac{{}^4{C}_1}{{}^{52}{C}_1}=\frac{1}{169}$

$P(x=1)+P(x=2)=\frac{25}{169}$.