A medical study recently documented that 905 mistakes were made among the 289,411 prescriptions written in one year at a large metropolitan teaching hospital. Suppose a patient is admitted with a condition serious enough to warrant ten different prescriptions. Approximate the probability that at least one will contain an error.

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A medical study recently documented that 905 mistakes were made among the 289,411 prescriptions written in one year at a large metropolitan teaching hospital. Suppose a patient is admitted with a condition serious enough to warrant ten different prescriptions. Approximate the probability that at least one will contain an error.

I know we are to use Poisson's limit approximation to the binomial in this problem, but is the n=289,411 or is it n=10?  I guess because of the large n=289,411 and small p=905/289,411 is what makes it a Poisson limit problem, but then how can we just switch to saying n=10?

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