Exactly one typo across two pages

Question

Typos are scattered through a manuscript as a Poisson process at rate $\lambda = 3$ per page. (A Poisson process can run over pages instead of time; the math is identical.)

What is the probability that a given two-page spread contains exactly $1$ typo?

Accepted Answer

Here the "window" is 2 pages instead of a time interval, but the recipe is the same. The mean number of typos across two pages is \mu = \lambda t = 3 	imes 2 = 6. So we expect about six typos on a two-page spread. The chance of exactly k = 1 typo is P(N = 1) = e^{-6}\,\frac{6^1}{1!} = 6\,e^{-6} \approx 6 	imes 0.002479 \approx 0.0149. Only about a 1.5\% chance of exactly one, because with an average of six, seeing just one would be unusually clean. Takeaway. Poisson processes work over any measure, time, length, or area; convert the rate to the mean count \mu = \lambda t over the relevant s…

Exactly one typo across two pages

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