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KVPY Sample Paper KVPY Stream-SX Model Paper-3

  • 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 \[\text{P}(X=1)+\text{P}\,(X=2)\] equals:

    A) \[\frac{52}{169}\]                                 

    B) \[\frac{25}{169}\]

    C) \[\frac{49}{169}\]                                 

    D) \[\frac{24}{169}\]

    Correct Answer: B

    Solution :

    \[p=\frac{4}{52}=\frac{1}{13}\] \[\Rightarrow \]\[q=\frac{12}{13}\] \[n=2.p(x=k)={}^{n}{{C}_{k}}.{{q}^{x-k}}.{{p}^{k}}\] \[p(x=1)+p(x=2)={}^{2}{{C}_{1}}\frac{12}{13}.\frac{1}{13}+{}^{2}{{C}_{2}}{{\left( \frac{1}{13} \right)}^{2}}=\frac{25}{169}.\]


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