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. 52/169
• B. 25/169
• C. 49/169
• D. 24/169

Answer 1

Answer: (B)

25/169

Answer 2

Two cards are drawn successively with replacement 4 Aces 48 Non Aces $P\left(x=1\right) = \frac{^{4}C_{1}}{^{52}C_{1}} \times\frac{48C_{1}}{52C_{1}} + \frac{48C_{1}}{52C_{1}}+\frac{4C_{1}}{52C_{1}} = \frac{24}{169}$ $P\left(x=2\right) = \frac{^{4}C_{1}}{^{52}C_{1}} \times\frac{^{4}C_{1}}{^{52}C_{1}} = \frac{1}{169}$ $P\left(x=1\right)+P\left(x=2\right)= \frac{25}{169}$