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### The Probability of Misprints: Background

Misprints plague us all. To remove misprints we read and reread, and we try to coerce others into reading. The issue is, when can we declare victory?

In this article we do two things: first, we summarize the background for determining the probability distribution of misprints in a manuscript, then we provide a table of the distribution function from which you may determine the probabilities for misprints in your manuscript.

Let n represent a number of misprints per page and let Pn be the probability of finding n misprints on any page. We assume the following:

1. Each misprint is a single, discrete, random event. If you consistently misspell separate, then that is a systematic error, not a random one. Presumably, your spell-checker has already found those kinds of errors. But if you consistently use their, when you should be using there, then your spell-checker fails to help and this error is also systematic.
2. Each misprint is independent of all other misprints. If you inadvertently type recieve, then you have two typos: the i and the second e are misplaced. But these two errors are not independent, and you should count this as a single independent misprint.
3. The probabilities Pn are properly normalized and they lie between 0 and 1.
4. The probability Pn, for any n of interest, is small. If you are particularly prone to misprints, the following analysis may not apply until you have corrected many of them.

There are a couple of other more technical assumptions, but they rarely apply for our problem, so I will not bother you with them. In our situation, the original question (When victory?), therefore, really has to do with the probability of rare events; events that are expected to occur infrequently, but which have an impact when they do occur.

Under these assumptions, the probability Pn for n misprints per page is given by the Poisson distribution,

Pn = kn exp[– k]/n!

where k = average number of misprints per page. When the average k gets large, then the Poisson distribution collapses to a Gaussian. To compute a probability from the Poisson distribution, you must collect some data from your ms; in particular, you need an estimate for k.

##### References

R. W. Hamming, The Art of Probability for Scientists and Engineers, Addison-Wesley, Redwood, CA, 1991.

W. E. Deming, Some Theory of Sampling, Dover, New York, 1966; reprint of 1950 edition published by Wiley.