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JEE Main & Advanced Mathematics Probability Question Bank Conditional probability bayes theorem

  • question_answer
    Two cards are drawn one by one from a pack of cards.  The probability of getting first card an ace and second a colored one is (before drawing second card first card is not placed again in the pack)                                       [UPSEAT 1999; 2003]

    A)                 \[\frac{1}{26}\]    

    B)                 \[\frac{5}{52}\]

    C)                 \[\frac{5}{221}\]  

    D)                 \[\frac{4}{13}\]

    Correct Answer: C

    Solution :

               \[P({{E}_{1}})=\frac{4}{52}=\frac{1}{13}\], \[P\left( \frac{{{E}_{2}}}{{{E}_{1}}} \right)=\frac{15}{51}=\frac{5}{17}\]                 \[P({{E}_{1}}\cap {{E}_{2}})=P({{E}_{1}}).P\,\left( \frac{{{E}_{2}}}{{{E}_{1}}} \right)=\frac{1}{13}.\,\frac{5}{17}=\frac{5}{221}\].


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