Suppose that the occurrence of typographical errors in the first draft of a book is well approximated as a Poisson process with a rate of 1 error per 1000 words. Each time the author proofreads the...

Suppose that the occurrence of typographical errors in the first draft of a book is well approximated as a Poisson process with a rate of 1 error per 1000 words. Each time the author proofreads the book, the error rate is reduced by 50%. For example, after the first proofreading, the error rate is 0.5 errors per 1000 words, or 1 error per 2000 words. Notice that we are saying that the “error rate” goes down by 50%, not that the actual number of errors is reduced by that amount since the author can (and did) introduce new errors while correcting other errors. The author wants to know how many times he needs to proofread the book so that the probability of there being no errors is at least 0.98. Assume that the book contains 200,000 words. Compute this number.