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

Answer 1

The correct option is B $\frac{25}{169}$

For X=1, the outcome of ace can be either in the first draw or the second draw.
Therefore, P(X=1) $=\frac{4}{52}\times \frac{48}{52}+\frac{48}{52}\times \frac{4}{52}$
$=2\times \frac{4}{52}\times \frac{48}{52}=\frac{24}{169}$
P(X=2) $=\frac{4}{52}\times \frac{4}{52}=\frac{1}{169}$
Then, P(X=1) + P(X=2) $=\frac{24}{169}+\frac{1}{169}=\frac{25}{169}$