The number of typographical errors in a document follows a Poisson distribution with a mean of 4 errors per page. Let $X$ represent the number of errors on 2 pages. Find $P ($ Less than 3).
A) 0.0138
B) 0.2381
C) 0.0030
D) 0.0134

Question

Quizplus · Accepted Answer

The probability of less than 3 errors on 2 pages is the sum of the probabilities of 0, 1, and 2 errors. Using the Poisson distribution with a mean of 4 errors per page, we have:$$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$$$$= e^{-8} \frac{8^0}{0!} + e^{-8} \frac{8^1}{1!} + e^{-8} \frac{8^2}{2!}$$$$= 0.0003 + 0.0024 + 0.0110 = 0.0137$$Therefore, the probability of less than 3 errors on 2 pages is 0.0137, which is closest to choice A, 0.0138.

The Number of Typographical Errors in a Document Follows a Poisson