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JEE Main & Advanced JEE Main Paper (Held on 12-4-2019 Afternoon)

  • question_answer
    For and initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is\[\frac{4}{5},\] then the probability that he is unable to solve less than two problems is : [JEE Main 12-4-2019 Afternoon]

    A) \[\frac{316}{25}{{\left( \frac{4}{5} \right)}^{48}}\]                     

    B) \[\frac{54}{5}{{\left( \frac{4}{5} \right)}^{49}}\]

    C) \[\frac{164}{25}{{\left( \frac{1}{5} \right)}^{48}}\]                     

    D) \[\frac{201}{5}{{\left( \frac{1}{5} \right)}^{49}}\]

    Correct Answer: B

    Solution :

    Let X be random varibale which denotes number of problems that candidate is unbale to solve \[\because \]\[p=\frac{1}{5}\]and\[X<2\] \[\Rightarrow P(X<2)=P(X=0)+P(X=1)\] \[={{\left( \frac{4}{5} \right)}^{50}}+{}^{50}{{C}_{1}}.\left( \frac{1}{5} \right).{{\left( \frac{4}{5} \right)}^{49}}\]


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