Probability of misprints

Question Q6.7.4

Suppose an $n$-page book is known to contain $m$ misprints. If the misprints are independent of one another, the probability of a misprint occuring on a particular page is $p=1/n$ and their distribution may be considered to be binomial. Write a short program to conduct a number of trial virtual "printings" of a book with $n=500, m=400$ and determine the probability, $\mathrm{Pr}$, that a single given page will contain misprints.

Compare with the result predicted by the Poisson distribution with rate parameter $\lambda = m/n$, $\mathrm{Pr} = 1 - e^{-\lambda}\left(\frac{\lambda^0}{0!} + \frac{\lambda}{1!}\right)$.


Solution

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