Answer to Question #339171 in Statistics and Probability for Tushal

Question

Suppose a book of 585 pages contains 43 types of graphical errors if these errors are randomly distributed throughout the book .what is the probability that 10 pages selected at random will be free from errors

Answer 1

Let $X=$number of errors per page. Assume that Poisson law holds for the number of errors per page: $X\sim Po(\lambda).$

Given $p=43/585, n=10.$ Then $\lambda=np=\dfrac{43}{585}(10)\approx0.735.$

$$P(X=0)=\dfrac{e^{-0.735}(0.735)^0}{0!}\approx0.4795$$