JEE Main & Advanced AIEEE Solved Paper-2006

  • question_answer
    At a telephone enquiry system, the number of phone calls regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10 min time intervals. The probability that there is atmost one phone call during a 10 min time period, is     AIEEE  Solved  Paper-2006

    A) \[\frac{5}{6}\]           

    B)                        \[\frac{6}{55}\]

    C) \[\frac{6}{{{e}^{5}}}\]                   

    D)        \[\frac{6}{{{5}^{e}}}\]

    Correct Answer: C

    Solution :

    Required probability \[=P(X=0)+P(X=1)\] \[=\frac{{{e}^{-5}}}{0!}{{5}^{0}}+\frac{{{e}^{-5}}}{1!}{{.5}^{1}}\] \[={{e}^{-5}}+5{{e}^{-5}}=\frac{6}{{{e}^{5}}}\]

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