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  4. 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 minute time intervals. The probability that there is at the most one phone call during a 10 minute time period, is :

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Q. 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 minute time intervals. The probability that there is at the most one phone call during a 10 minute time period, is :

AIEEEAIEEE 2006Probability - Part 2

Solution:

Required probability $= P (X = 0)+ P (X = 1)$
$=\frac{e^{-5}}{0\,!}5^{0}+\frac{e^{-5}}{1\,!}\cdot5^{1}$
$=e^{-5}+5e^{-5}$
$=\frac{6}{e^{5}}$