Question

A book with 1400 pages has 700 typos. Under assumptions that one should find reasonable, determine the probability that a page has 2 typos.

Answer 1

assuming you meant "Typos in a book," haha.

You should use the Poisson distribution. The Poisson distribution is appropriate when there are a fixed large number of trials in a given interval (a page, in this case) and each trial has a fixed (usually low) probability. The product of the number of trials and the probability of success (or typo) in each trial is the rate λ of the Poisson distribution.

ETA: In the limit, as λ increases without bound, the distribution does approach a normal distribution. At λ=10, here, the difference is not profound, but it's still more appropriate to use the Poisson distribution.

In actual fact, since the number of characters on a page (i.e., the number of trials on a page) is finite, it might be even more appropriate to use a binomial distribution. However, the difference between the binomial distribution and the Poisson distribution is not significant at this scale, and the Poisson distribution is far easier to compute.