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 $\mathrm{P}(\mathrm{X}=1)+\mathrm{P}(\mathrm{X}=2)$ equals :
Correct Option: , 2
Two cards are drawn successively with replacement
4 Aces 48 Non Aces
$\mathrm{P}(\mathrm{x}=1)=\frac{{ }^{4} \mathrm{C}_{1}}{{ }^{52} \mathrm{C}_{1}} \times \frac{48 \mathrm{C}_{1}}{52 \mathrm{C}_{1}}+\frac{48 \mathrm{C}_{1}}{52 \mathrm{C}_{1}} \times \frac{4 \mathrm{C}_{1}}{52 \mathrm{C}_{1}}=\frac{24}{169}$
$\mathrm{P}(\mathrm{x}=2)=\frac{{ }^{4} \mathrm{C}_{1}}{{ }^{52} \mathrm{C}_{1}} \times \frac{{ }^{4} \mathrm{C}_{1}}{{ }^{52} \mathrm{C}_{1}}=\frac{1}{169}$
$P(x=1)+P(x=2)=\frac{25}{169}$