Originally Posted by

**James0502** A textbook has n pages. The number of mistakes on a page is a poisson random variable with parameter a, and is independent of the number of mistakes on all other pages. What is the expected number of pages with no mistakes?

I get this as n*e^-a

When reading the book you detect each mistake with probability p, independently of other mistakes. Let M denote the number of mistakes on a particular page and let D denote the number of mistakes detected. Write down P[D = k|M = m]

I modelled on binomial, parameters m and p

so = m choose k * p^k(1-p)^(m-k)

Hence find, for each k >/= 0 P[D=k]

I'm not sure how to start this part

many thanks