Question

Assume the number of typo errors on a single page of a book follows Poisson distribution with parameter 1=3. Calculate the probability that on one page there are (i) exactly 2 typos (ii) two or more typo?

Answer 1

Answer:

(i). 0.03981

(ii).0.0048

Step-by-step explanation:

The probability density function of Poisson distribution is:

$P(X=x,\lambda)=\frac{e^{-\lambda}\lambda^x}{x!} \; \;\;\,\; x=0,1,2,...$

Consider X is a number of typos error on a single page of a book and X follows the Poisson distribution with $\lambda = \dfrac{1}{3}$

(i) Exactly two typos:

            $\begin{aligned}P(X = 2,\frac{1}{3})&=\frac{e^{-\frac{1}{3}}\frac{1}{3}^{2}}{2!}\\&=\frac{e^{-\frac{1}{3}}}{18}\\&=0.03981\end{aligned}$

(ii) Two or more typos:

       $\begin{aligned}P(X\geq2,\frac{1}{3})&=1-[P(X=0)+P(X=1)+P(X+2)]\\&=1-[0.7165+0.2388+0.03981]\\&=1-0.9952\\&=0.0048\end{aligned}$