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JEE Main & Advanced Mathematics Probability Question Bank Mock Test - Probability

  • question_answer
    A man has 3 pairs of black socks and 2 pairs of brown socks kept together in a box. If he dressed hurriedly in the dark, the probability that after he has put on a black sock, he will then put on another black sock is

    A) 1/3       

    B) 2/3

    C) 3/5       

    D) 2/15

    Correct Answer: A

    Solution :

    [a] \[P({{B}_{1}})=\frac{^{6}{{C}_{1}}}{^{6}{{C}_{1}}}=\frac{6}{10}=\frac{3}{5}\] \[P({{B}_{2}}/{{B}_{1}})=\frac{5}{9}({{B}_{2}}=black)\] \[\therefore P({{B}_{1}}\cap {{B}_{2}})=P({{B}_{1}})P({{B}_{2}}/{{B}_{1}})=\frac{3}{5}\times \frac{5}{9}=\frac{1}{3}\]


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