MHT CET · Maths · Probability
Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Let X denote the random variable of number of jacks obtained in the two drawn cards. Then \(\mathrm{P}(\mathrm{X}=1)+\mathrm{P}(\mathrm{X}=2)\) equals
- A \(\frac{24}{169}\)
- B \(\frac{52}{169}\)
- C \(\frac{25}{169}\)
- D \(\frac{49}{169}\)
Answer & Solution
Correct Answer
(C) \(\frac{25}{169}\)
Step-by-step Solution
Detailed explanation
Since two cards are drawn successively with replacement, we get
\(P(X=1)=2 \times \frac{{ }^4 C_1 \times{ }^{48} C_1}{{ }^{52} C_1 \times{ }^{52} C_1}=2 \times \frac{4 \times 48}{52 \times 52}=\frac{24}{169}\)
\(\begin{aligned} & P(X=2)=\frac{{ }^4 C_1 \times{ }^4 C_1}{{ }^{52} C_1 \times{ }^{51} C_1}=\frac{4 \times 4}{52 \times 52}=\frac{1}{169} \\ \therefore \quad & P(X=1)+P(X=2)=\frac{25}{169}\end{aligned}\)
\(P(X=1)=2 \times \frac{{ }^4 C_1 \times{ }^{48} C_1}{{ }^{52} C_1 \times{ }^{52} C_1}=2 \times \frac{4 \times 48}{52 \times 52}=\frac{24}{169}\)
\(\begin{aligned} & P(X=2)=\frac{{ }^4 C_1 \times{ }^4 C_1}{{ }^{52} C_1 \times{ }^{51} C_1}=\frac{4 \times 4}{52 \times 52}=\frac{1}{169} \\ \therefore \quad & P(X=1)+P(X=2)=\frac{25}{169}\end{aligned}\)
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