At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson…

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
  1. $\frac{6}{5^{\mathrm{e}}}$
  2. $\frac{5}{6}$
  3. $\frac{6}{55}$
  4. $\frac{6}{e^5}$

Solution

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

Asked in: JEE Main 2006

Practice more Probability questions on Aicharya