Two cards are drawn successively with replacement from a well- shuffled pack of 52. cards. Let X denote the…
Two cards are drawn successively with replacement from a well- shuffled pack of 52. cards. Let X denote the random variable of number of kings obtained in the two drawn cards. Then $\mathrm{P}(x=1)+\mathrm{P}(x=2)$ equals
$\frac{49}{169}$
$\frac{24}{169}$
$\frac{52}{169}$
$\frac{25}{169}$
Solution
Probability of getting an king card is $\frac{4}{52}$
For $\mathrm{X}=1$, the outcome of king can be either in first draw of the second draw.
$\begin{aligned}
& \therefore \quad \mathrm{P}(\mathrm{X}=1)=\frac{4}{52} \times \frac{48}{52}+\frac{48}{52} \times \frac{4}{52} \\
& =2 \times \frac{4}{52} \times \frac{48}{52}=\frac{24}{169} \\
& \therefore \quad \mathrm{P}(\mathrm{X}=2)=\frac{4}{52} \times \frac{4}{52}=\frac{1}{169} \\
& \therefore \quad \mathrm{P}(\mathrm{X}=1)+\mathrm{P}(\mathrm{X}=2)=\frac{24}{109}+\frac{1}{169}=\frac{25}{169}
\end{aligned}$