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

  • question_answer
    A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is                                                               [UPSEAT 2004]

    A)            \[\frac{14}{15}\]                     

    B)            \[\frac{11}{15}\]

    C)            \[\frac{7}{15}\]                       

    D)            \[\frac{4}{15}\]

    Correct Answer: C

    Solution :

                       Required probability                    = Either the balls are red or the balls are black            \[=\frac{^{8}{{C}_{2}}}{^{15}{{C}_{2}}}+\frac{^{7}{{C}_{2}}}{^{15}{{C}_{2}}}=\frac{28+21}{105}\]\[=\frac{49}{105}=\frac{7}{15}\].


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