Question

A book contains 400 pages. If their are 80 typing errors randomly distributed throughout the book, use the Poisson distribution to determine the probability that a page contains exactly 2 errors

Answer 1

Using the Poisson distribution to determine the probability that a page contains exactly 2 errors is 0.0163

Solution:

Given that, a book contains 400 pages.

There are 80 typing errors randomly distributed throughout the book,

We have to use the Poisson distribution to determine the probability that a page contains exactly 2 errors.

The Poisson distribution formula is given as:

$\text { Probability distribution }=e^{-\lambda} \frac{\lambda^{k}}{k !}$

Where, $\lambda$ is event rate of distribution. For observing k events.

$\text { Here rate of distribution } \lambda=\frac{\text { go mistakes }}{400 \text { pages }}=\frac{1}{5}$

And, k = 2 errors.

$\begin{array}{l}{\text { Then, } \mathrm{p}(2)=e^{-\frac{1}{5}} \times \frac{\frac{1}{5}}{2 !}} \\\\ {=2.7^{-\frac{1}{5}} \times \frac{\frac{1}{5^{2}}}{2 \times 1}} \\\\ {=\frac{1}{2.7^{\frac{1}{5}}} \times \frac{\frac{1}{25}}{2}}\end{array}$

$\begin{array}{l}{=\frac{1}{\sqrt[5]{2.7}} \times \frac{1}{25} \times \frac{1}{2}} \\\\ {=\frac{1}{50 \sqrt[5]{2.7}}} \\\\ {=0.0163}\end{array}$

Hence, the probability is 0.0163