Poisson distribution probability question

Question

The typos on a page in magazine has a Poisson distribution. The probabilty of a page having typo(s) is 0.2.

What is the probabilty that there are exactly 3 typos on a page?

Thanks in advance!

Answer 1

First we need to calculate the parameter of the Poisson distribution. Call the Poisson random variable X.

We have

$$ 0.8 = P(X = 0) = e^{-\lambda},$$

using the definition of the Poisson distribution.

Hence $ \lambda = -\log(0.8) = \log(5/4)$.

So $ \ \ \ P(X=3) = \dfrac{(\log(5/4))^3 e^{-\log((5/4))}}{3!} =\dfrac{2(\log(5/4))^3 }{15}. $