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JEE Main & Advanced Mathematics Probability Question Bank Self Evaluation Test - Probability-II

  • question_answer
    A problem in mathematics is given to three students, A, B, C and their respective probability of solving the problem is\[\frac{1}{2}\], \[\frac{1}{3}\]and\[\frac{1}{4}\]. Probability that the problem is solved is

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

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

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

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

    Correct Answer: A

    Solution :

    [a] \[P({{E}_{1}})=\frac{1}{2},P({{E}_{2}})=\frac{1}{3}andP({{E}_{3}})=\frac{1}{4};\] \[P({{E}_{1}}U{{E}_{2}}U{{E}_{3}})=1-P(\overline{{{E}_{1}}})P(\overline{{{E}_{2}}})P(\overline{{{E}_{3}}})\] \[=1-\left( 1-\frac{1}{2} \right)\left( 1-\frac{1}{3} \right)\left( 1-\frac{1}{4} \right)=\frac{3}{4}\]


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