I wouldn't use a probability density of typo's per page, but instead the probability that a word is spelled wrong. Then it's like drawing marbles from a vase c

I wouldn't use a probability density of typo's per page, but instead the probability that a word is spelled wrong. Then it's like drawing marbles from a vase containing an unknown proportion of blue and red marbles. I would use the formula (M+1)/(N+2) where N is the number of words, and M is the number of mistakes. Note that for a large corpus (M+1)/(N+2) approaches -> M/N, so we recover the frequentist probability. Also note the author (John D Cook) correctly expresses intuitive doubt that 0 typos / 20 pages can not be construed as certainty of no mistakes. Similarily, seeing a mistake in every word in a subset does not guarantee that all words in the book will have a typo. Let's look at the modified formula (M+1)/(N+2) in these cases: if we observe no typos (M=0) in 1000 words, it estimates the typo probability as (0+1)/(1000+2)=1/1002 != 0, so we can't rule out mistakes. Similarily if all words were typos (M=N) for the first 1000 words we get 1001/1002 != 1, so we can't be sure every future word is a typo. Check out Norman D Megill's paper on "Estimating Bernoulli trial probability from a small sample" where the formula (M+1)/(N+2) is derived, on page 3 it appears: https://arxiv.org/abs/1105.1486 https://arxiv.org/abs/1105.1486