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

  • question_answer
    Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman is                                                            [ISM Dhanbad 1994]

    A)            \[\frac{25}{39}\]                     

    B)            \[\frac{14}{39}\]

    C)            \[\frac{5}{13}\]                       

    D)            \[\frac{10}{13}\]

    Correct Answer: A

    Solution :

               Required probability \[=\frac{{}^{5}{{C}_{1}}\times {}^{8}{{C}_{1}}}{{}^{13}{{C}_{2}}}+\frac{{}^{5}{{C}_{2}}}{{}^{13}{{C}_{2}}}=\frac{25}{39}.\]


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