Q67 / 150 · JEE Main 2006 · Mathematics

At a telephone enquiry system the number of phone cells 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

  • A
    $\frac{6}{5^{\mathrm{e}}}$
  • B
    $\frac{5}{6}$
  • C
    $\frac{6}{55}$
  • Correct answer
    D
    $\frac{6}{e^5}$

Solution

$P(X=r)=\frac{e^{-m} m^r}{r !}$ $P(X \leq 1)=P(X=0)+P(X=1)$ $=e^{-5}+5 \times e^{-5}=\frac{6}{e^5}$

Hence, the correct answer is option: 'D'.

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