Question

Suppose 300 misprints are randomly distributed throughout a book of 500 pages, find the probability that a given page contains exactly 4 misprints.

Answer 1

Given that,

Misprints = 300

Pages of book = 500

We need to calculate the value of λ

Using formula of λ

$\lambda=\dfrac{number\ of\ misprints}{number\ of\ pages}$

Put the value into the formula

$\lambda=\dfrac{300}{500}$

$\lambda=0.6$

We need to calculate the probability

Using formula of probability

$P(x)=\dfrac{e^{-\lambda}\times(\lambda)^{x}}{x!}$

For x=4,

Put the value of x

$P(4)=\dfrac{e^{-0.6}\times(0.6)^{4}}{4!}$

$P(4)=0.0029$

Hence, The probability is 0.0029.