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JEE Main & Advanced Mathematics Probability Question Bank Use of permutations and combinations in probability

  • question_answer
    A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random. The probability that at least one of these is an ace, is                                               [MNR 1991]

    A)            \[\frac{9}{20}\]                       

    B)            \[\frac{3}{16}\]

    C)            \[\frac{1}{6}\]                          

    D)            \[\frac{1}{9}\]

    Correct Answer: A

    Solution :

                       Required probability is \[1-P\] (No Ace)                                                                       \[=1-\frac{{}^{12}{{C}_{2}}}{{}^{16}{{C}_{2}}}=1-\frac{12\,\,.\,\,11}{16\,\,.\,\,15}=\frac{9}{20}.\]


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