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

  • question_answer
    A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. One fruit is picked out from each basket. Find the probability that the fruits are both apples or both oranges                               [AMU 2002]

    A)            \[\frac{24}{144}\]                   

    B)            \[\frac{56}{144}\]

    C)            \[\frac{68}{144}\]                   

    D)            \[\frac{76}{144}\]

    Correct Answer: D

    Solution :

                       Required probability                    \[=\frac{^{5}{{C}_{1}}{{\,}^{4}}{{C}_{1}}}{^{12}{{C}_{1}}^{12}{{C}_{1}}}+\frac{^{7}{{C}_{1}}{{\,}^{8}}{{C}_{1}}}{^{12}{{C}_{1}}{{\,}^{12}}{{C}_{1}}}\]\[=\frac{20+56}{144}=\frac{76}{144}\].


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