Suppose a book with 100 pages is divided into 5 chapters of 20 pages each. The book contains 10 typos distributed randomly amongst the pages.

Question

(a) What is the probability that Page# 89 has exactly 2 typos?

I know this is a poison distribution question, and the rate happens to be 0.1 typos/page, but I'm having trouble on how I would figure out specifically the probability for page 89 having 2 typos.

Answer 1

What's the probability that the first and second error both occur on page #89? Assuming no correlation, it's $(0.01)^2 = 0.0001$.

What's the probability that any two specific errors occurs on page #89? It's $0.0001$.

Assuming that exactly two of the ten errors occurs on page #89, how many different ways could this occur? That's ${}_{10}C_{2} = 45$.

So, the probability is: $$ P = (45)(0.0001) = 0.0045 $$