Given that the average number of typos per page is 4, what is the probability of 1 typo on a page?

Question

Typing errors or “typos” occur at random on pages in books. The occurrence of these typos are
independent of each other. We can safely assume that the occurrence of typos actually has a
rather small probability otherwise typing would be rather useless. Denote the number of typos
on a page by the R.V. X. Given that the average number of typos per page is 4, what is the
probability of 1 typo on a page?

Answer 1

This is a discrete Poisson distribution. The mean is Lambda, which has been given to you as 4.

 

Therefore you just need to evaluate P(k errors/page) = p_k = λ^ke^-λ/k! where k = 0, 1, 2, etc for # errors per page.

In this problem, use k=1.