JEE Mains · Maths · STD 12 - 13. probability
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 \(P\,\left( {X = 1} \right)\, + P\,\left( {X = 2} \right)\) equals
- A \(\frac{{49}}{{169}}\)
- B \(\frac{{52}}{{169}}\)
- C \(\frac{{24}}{{169}}\)
- D \(\frac{{25}}{{169}}\)
Answer & Solution
Correct Answer
(D) \(\frac{{25}}{{169}}\)
Step-by-step Solution
Detailed explanation
\(P(x=1)=\frac{4}{52} \times \frac{48}{52} \times 2=\frac{24}{169}\) \(P(x=2)=\frac{4}{52} \times \frac{4}{52}=\frac{1}{169}\) \(\Rightarrow P(x=1)+P(x+2)=\frac{25}{169}\)
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