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

  • question_answer
    A man draws a card from a pack of 52 playing cards, replaces it and shuffles the pack. He continues this processes until he gets a card of spade. The probability that he will fail the first two  times  is                                           [MNR 1980]

    A)            \[\frac{9}{16}\]                       

    B)            \[\frac{1}{16}\]

    C)            \[\frac{9}{64}\]                       

    D)            None of these

    Correct Answer: C

    Solution :

                       The required probability is given by                    \[\frac{{}^{39}{{C}_{1}}}{{}^{52}{{C}_{1}}}\times \frac{{}^{39}{{C}_{1}}}{{}^{52}{{C}_{1}}}\times \frac{{}^{13}{{C}_{1}}}{{}^{52}{{C}_{1}}}=\frac{3}{4}\times \frac{3}{4}\times \frac{1}{4}=\frac{9}{64}.\]


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