Question

In a book of 450 pages, there are 400 typographical errors, Assuming that the number of error per page follow the Poisson law. Find the probability of random sample of 5 pages will contain no typographical errors.

Answer 1

Answer: total no of no typographical errors=50

Total no of event occurs =5

P(A)=5/50

P(A)=1/10

P(A)=0.1

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Step-by-step explanation:

Answer 2

The probability of random sample of 5 pages will contain no typographical errors is [e^(-8/9)]^5

Given that, there are 400 typological errors in a book of 450 pages.

Therefore, the average number of errors per page in a book = 400/450

= 8/9

To find the probability that a sample of 5 pages will contain no errors.

So, P(X=r) = (e^-λ)(λ^r)/r!

So, r should be equal to zero because we have to find zero errors.

And λ as calculated above = 8/9

Replacing the values, we get

P(X=0) = (e^-[8/9])([8/9]^0)/0!

= e^(-8/9)

For 5 pages, it would be = [e^(-8/9)]^5