Probability and Poisson distribution

1k Views Asked by At

Suppose that a book contains an average of $\lambda$ misprints per page.

(a) What is the probability that $10$ pages will contain at most $1$ misprint?

(b) What is the probability that $n$ pages will contain at most $3$ misprints?

(c) If the book has $n$ pages, what is the probability that there will be at least $m$ pages that each contain more than $k$ misprints?

I am not sure how to approach this question. Does it have to do with Poisson distribution?

1

There are 1 best solutions below

0
On

Hint 1: If $X$ is the number of misprints on $n$ pages, then $X\sim\text{Poisson}(n\lambda)$.

Hint 2: If $X\sim\text{Poisson}(\lambda)$ and $Y$ is the number of pages with more than $k$ misprints then $Y\sim\text{Binomial}(n,p=P(X>k))$.