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

  • question_answer
    A box contains 10 mangoes out of which 4 are rotten. 2 mangoes are taken out together. If one of them is found to be good, the probability that the other is also good is [EAMCET 1992]

    A)            \[\frac{1}{3}\]                          

    B)            \[\frac{8}{15}\]

    C)            \[\frac{5}{18}\]                       

    D)            \[\frac{2}{3}\]

    Correct Answer: C

    Solution :

                       Number of ways of selecting two good mangoes = \[^{6}{{C}_{2}}=15\]. Number of ways that at least one of the two selected mangoes is to be good \[={}^{6}{{C}_{1}}\times {}^{9}{{C}_{1}}=54\]                    \[\therefore \] Required probability \[=\frac{15}{64}=\frac{5}{18}\].


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