### Function of an appropriate random variable

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Suppose you work for an insurance company. 3,000,000 people in Georgia took out car insurance. Suppose in each year, that any of the given 3,000,000 people involves in a car accidence with probability 10−5 , independent of all else. Suppose that any one involved in a car accidence may or may not claim, and say that each of them claim to your company with probability 0.8, independent of all else. Suppose you pay each claimed case 1000 dollars.

Express the total amount of money M your company must pay out as a function of an appropriate random variable, and then compute approximately the probabilty that M = 5000.

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