Question

A book containing 150 pages has 100 misprints. Find the probability that a particular

page contains (a) no misprints, (b) 5 misprints, (c) at least 2 misprints, (d) more than 1

misprint.

Answer 1

Let $X=$ the number of misprints per page: $X\sim Po(\lambda).$

$\lambda=\dfrac{100}{150}=\dfrac{2}{3}$

(a)

$$P(X=0)=\dfrac{e^{-2/3}(\dfrac{2}{3})^0}{0!}=e^{-2/3}\approx0.513417$$

(b)

$$P(X=5)=\dfrac{e^{-2/3}(\dfrac{2}{3})^5}{5!}\approx0.000563$$

(c)

$$P(X\geq2)=1-P(X=0)-P(X=1)$$

$$=1-\dfrac{e^{-2/3}(\dfrac{2}{3})^0}{0!}-\dfrac{e^{-2/3}(\dfrac{2}{3})^1}{1!}\approx0.144305$$

(d)

$$P(X>1)=P(X\geq2)=1-P(X=0)-P(X=1)$$

$$=1-\dfrac{e^{-2/3}(\dfrac{2}{3})^0}{0!}-\dfrac{e^{-2/3}(\dfrac{2}{3})^1}{1!}\approx0.144305$$