Answer:
a) The probability that an article of 10 pages contains 0 typographical errors is 0.8187.
b) The probability that an article of 10 pages contains 2 or more typographical errors is 0.0175.
Step-by-step explanation:
Given : The expected number of typographical errors on a page of a certain magazine is 0.2.
To find : What is the probability that an article of 10 pages contains
(a) 0 and (b) 2 or more typographical errors?
Solution :
Applying Poisson distribution,


where, n is the number of words in a page
and p is the probability of every word with typographical errors.
Here, n=10 and E(N)=np=0.2
a) The probability that an article of 10 pages contains 0 typographical errors.
Substitute r=0 in formula,




The probability that an article of 10 pages contains 0 typographical errors is 0.8187.
b) The probability that an article of 10 pages contains 2 or more typographical errors.
Substitute
in formula,

![P(N\geq 2)=1-[P(N=0)+P(N=1)]](https://tex.z-dn.net/?f=P%28N%5Cgeq%202%29%3D1-%5BP%28N%3D0%29%2BP%28N%3D1%29%5D)
![P(N\geq 2)=1-[\frac{e^{-0.2}(0.2)^0}{0!}+\frac{e^{-0.2}(0.2)^1}{1!}]](https://tex.z-dn.net/?f=P%28N%5Cgeq%202%29%3D1-%5B%5Cfrac%7Be%5E%7B-0.2%7D%280.2%29%5E0%7D%7B0%21%7D%2B%5Cfrac%7Be%5E%7B-0.2%7D%280.2%29%5E1%7D%7B1%21%7D%5D)
![P(N\geq 2)=1-[e^{-0.2}+e^{-0.2}(0.2)]](https://tex.z-dn.net/?f=P%28N%5Cgeq%202%29%3D1-%5Be%5E%7B-0.2%7D%2Be%5E%7B-0.2%7D%280.2%29%5D)
![P(N\geq 2)=1-[0.8187+0.1637]](https://tex.z-dn.net/?f=P%28N%5Cgeq%202%29%3D1-%5B0.8187%2B0.1637%5D)


The probability that an article of 10 pages contains 2 or more typographical errors is 0.0175.