In some book, $250$ misprints are randomly and independently distributed on $500$ pages. What is the probability that there are no misprints on the first three pages?
I'm not sure how to solve this. Is using binomial distribution and adding the probabilities $P_1, P_2, P_3$ where $P_1$ is the probability that there is no misprint on the first page, $P_2$ on the second page and so on a good approach? How would you solve this problem? Any help would be much appreciated.
Best Answer
It's not binomial. That we be correct if it were a case of sampling without replacement, but nothing says we can't have more than one misprint on a page. So a model of the problem is: we draw a number from $1$ to $500$ at random $250$ times. What is the probability that we never draw the number $1,\ 2\text{ or }3$?
Can you do it now?