Question

A car hire firm has $2$ cars which it hires out day by day. If the number of demands for a car on each day follows Poisson distribution with parameter $1.5$, then the probability that both the cars is used is

• A. $1.12\times e^{-1.5}$
• B. $1-2.5\times e^{-1.5}$
• C. $1-3.625\times e^{-1.5}$
• D. $3.625\times e^{-1.5}$

Answer 1

Answer: (B)

$1-2.5\times e^{-1.5}$

Here $\lambda =1$
Hence probability that both the cars are used $=1-P(X=0)-P(X=1)=1-\frac{e^{-1.5}(1.5{)}^0}{0!}-\frac{e^{-1.5}(1.5{)}^1}{1!}=1-2.5e^{-1.5}$