JEE Main & Advanced Mathematics Probability Question Bank Definition of probability

  • question_answer
    A problem in Mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2, 1/3 and 1/4.  Probability that the problem is solved is [RPET 2001; AIEEE 2002]

    A)                 \[\frac{3}{4}\]       

    B)                 \[\frac{1}{2}\]

    C)                 \[\frac{2}{3}\]       

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

    Correct Answer: A

    Solution :

               Probability problem is not solved by \[A=\,1-\frac{1}{2}=\frac{1}{2}\]            Probability problem is not solved by \[B=1-\frac{1}{3}=\frac{2}{3}\]            Probability problem is not solved by \[C=1-\frac{1}{4}=\frac{3}{4}\]            Probability of solving the problem \[=1-P\] (not solved by any body)                 \ \[P=1-\frac{1}{2}.\,\,\frac{2}{3}.\,\frac{3}{4}\,=\,1-\frac{1}{4}=\frac{3}{4}\].


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