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.
Question 1: What is the expected number of pages with no mistakes?
I get this as n*e^-a
Question 2: 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)
Question 3: Hence find, for each k >/= 0 P[D=k]
I'm not sure how to start this part