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The number of times that an individual contracts a cold in a given year is a Poisson random variable with parameter λ = 5. Suppose a new wonder drug (based on large quantities of vitamin C) that has just been marketed reduces the Poisson parameter to λ = 3 for 75 percent of the population. For the other 25 percent of the population, the drug has no effect on colds. If an individual tries the drug for a year and has 2 colds in that time, what is the probability that the drug is beneficial to that individual?

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