JEE Main & Advanced Mathematics Probability Question Bank Binomial distribution

  • question_answer
    A man make attempts to hit the target. The probability of hitting the target is \[\frac{3}{5}.\] Then the probability that A hit the target exactly 2 times in 5 attempts, is

    A)                 \[\frac{144}{625}\]             

    B)                 \[\frac{72}{3125}\]

    C)                 \[\frac{216}{625}\]             

    D)                 None of these

    Correct Answer: A

    Solution :

               Probability of success \[(p)=\frac{3}{5}\Rightarrow q=1-p=\frac{2}{5}\]            Hence the probability of 2 hits in 5 attempts                                 \[={}^{5}{{C}_{2}}{{\left( \frac{3}{5} \right)}^{2}}{{\left( \frac{2}{5} \right)}^{3}}=\frac{144}{625}.\]


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