Answer to Question #188276 in Statistics and Probability for Tani Mog

Question

In a book of 520 pages, 390 typo

-graphical errors occur. Assuming Poisson law for the

number of errors per page, find the probability that a random sample of 5 pages will

contain no error.

Answer 1

The average number of typographical errors per page in the book is given by

$λ = \frac{390}{520} = 0.75$

Hence using Poisson probability law, the probability of x errors per page is given by:

$P(X=x) = \frac{e^{-λ}λ^x}{x!} \\ = \frac{e^{-0.75} \times (0.75)^x}{x!}$

The required probability that a random sample of 5 pages will contain no error is given by:

$[P(X=0)]^5 = (e^{-0.75})^5 = e^{-3.75}$