Question

An executive in a company makes on an average $5$ telephone calls per hour at a cost of $₹ 2$ per cell. The probability that in any hour the cost of the calls exceeds a sum of $₹ 4$ is

• A. $\frac{2 e^{4}-35}{2 e^{5}}$
• B. $\frac{2 e^{5}-37}{2 e^{5}}$
• C. $1-\frac{37}{e^{4}}$
• D. $1-(18.5) e^{5}$

Answer 1

Answer: (B)

The number of telephone calls per hour is a random variable with mean $=5$.
The required probability is given by
$ P(r>2)=1-P(r \leq 2)=1-\displaystyle \sum_{r=0}^{2} \frac{e^{-5} \cdot 5^{r}}{r !} $
$= 1-\left[\frac{5^{0}}{0 !}+\frac{5^{1}}{1 !}+\frac{5^{2}}{2 !}\right] \frac{1}{e^{5}}=1-\frac{37}{2 e^{5}}=\frac{2 e^{5}-37}{2 e^{5}}$