Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then the…
Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then the probability distribution of number of jacks is
- \begin{array}{|l|c|c|c|}
\hline \mathrm{X}=x & 0 & 1 & 2 \\
\hline \mathrm{P}(\mathrm{X}=x) & \frac{144}{169} & \frac{24}{169} & \frac{1}{169} \\
\hline
\end{array}
- \begin{array}{|l|c|c|c|}
\hline \mathrm{X}=x & 0 & 1 & 2 \\
\hline \mathrm{P}(\mathrm{X}=x) & \frac{1}{169} & \frac{144}{169} & \frac{24}{169} \\
\hline
\end{array}
- \begin{array}{|l|c|c|c|}
\hline \mathrm{X}=x & 0 & 1 & 2 \\
\hline \mathrm{P}(\mathrm{X}=x) & \frac{24}{169} & \frac{1}{169} & \frac{144}{169} \\
\hline
\end{array}
- \begin{array}{|c|c|c|c|}
\hline \mathrm{X}=x & 0 & 1 & 2 \\
\hline \mathrm{P}(\mathrm{X}=x) & \frac{144}{169} & \frac{1}{169} & \frac{24}{169} \\
\hline
\end{array}
Solution
Let $\mathrm{X}$ denotes the number of jacks
$\therefore \quad$ Possible values of $\mathrm{X}$ are $0,1,2$
$\therefore \quad \mathrm{P}(\mathrm{X}=0)=\frac{{ }^{48} \mathrm{C}_1 \times{ }^{48} \mathrm{C}_1}{{ }^{52} \mathrm{C}_1 \times{ }^{52} \mathrm{C}_1}=\frac{144}{169}$
$\begin{aligned}
& \mathrm{P}(\mathrm{X}=1)=\frac{{ }^{48} \mathrm{C}_1 \times{ }^4 \mathrm{C}_1}{{ }^{52} \mathrm{C}_1 \times{ }^{52} \mathrm{C}_1}+\frac{{ }^4 \mathrm{C}_1 \times{ }^{52} \mathrm{C}_1}{{ }^{52} \mathrm{C}_1 \times{ }^{52} \mathrm{C}_1}=\frac{24}{169} \\
& \mathrm{P}(\mathrm{X}=2)=\frac{{ }^4 \mathrm{C}_1 \times{ }^4 \mathrm{C}_1}{{ }^{52} \mathrm{C}_1 \times{ }^{52} \mathrm{C}_1}=\frac{1}{169}
\end{aligned}$
$\therefore \quad$ Option (A) is correct.
Asked in: MHT CET 2023 (12 May Shift 1)
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