JEE Main & Advanced Mathematics Probability Question Bank Definition of probability

  • question_answer
    ?A? draws two cards with replacement from a pack of 52 cards and ?B' throws a pair of dice what is the chance that ?A? gets both cards of same suit and ?B? gets total of 6 [MNR 1989]

    A)                 \[\frac{1}{144}\]  

    B)                 \[\frac{1}{4}\]

    C)                 \[\frac{5}{144}\]  

    D)                 \[\frac{7}{144}\]

    Correct Answer: C

    Solution :

               The probaility of drawing two cards of same suit \[=\frac{13}{52}\times \frac{13}{52}\] and it can be of any suit out of 4.            So \[P(A)=\frac{4\times 13\times 13}{52\times 52}=\frac{1}{4}\] and \[P(B)=\frac{5}{36}\]                 Thus \[P(A\cap B)=P(A)\,.\,P(B)=\frac{1}{4}\times \frac{5}{36}=\frac{5}{144}.\]


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