Question

In a book of $500$ pages, it is found that there are $250$ typing errors. Assume that Poisson law holds for the number of errors per page. Then, the probability that a random sample of $2$ pages will contain no error, is :

• A. $e^{-0.3}$
• B. $e^{-0.5}$
• C. $e^{-1}$
• D. $e^{-2}$

Answer 1

Answer: (C)

Here number of errors per page
$=\frac{250}{500}=\frac{1}{2}$
and $n=2$
$\therefore \lambda=n p=2 \times \frac{1}{2}=1$
and probability of no error
$P(X=0)=\frac{e^{-1} \times(1)^{0}}{0 !}=e^{-1}$