Question: A certain grammar-checking software searches for and finds grammatical mistakes according to the Poisson process at a mean rate of 5 mistakes per page. What

A certain grammar-checking software searches for and finds grammatical mistakes according to the Poisson process at a mean rate of 5 mistakes per page. What is the probability that the software will check less than half a page to find three grammatical mistakes? Use the gamma distribution and integration by parts twice to find the answer. Then find the same answer using a Poisson distribution. Round your answer to the fourth decimal.

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