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JEE Main & Advanced JEE Main Paper (Held On 09-Jan-2019 Morning)

  • question_answer
    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:  [JEE Main Online Paper (Held On 09-Jan-2019 Morning]

    A) 25/169

    B) 24/169

    C) 49/169

    D) 52/169

    Correct Answer: A

    Solution :

    \[P\left( X\text{ }=\text{ }1 \right)\text{ }+\text{ }P\left( X\text{ }=\text{ }2 \right)\] \[=\,\,\,\frac{4}{52}\,\times \,\frac{48}{52}\,\,\times \,\,2\,\,+\,\,\frac{4}{52}\,\,\times \,\,\frac{4}{52}\] \[=\,\,\,\,2\,\,\times \,\,\frac{12}{{{(13)}^{2}}}\,\,+\,\,{{\left( \frac{1}{13} \right)}^{2}}\] \[=\,\,\frac{25}{169}\]


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