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An insurance company insures two types of vehicles, popular vehicles and vehicles luxurious. The damages claimed...

An insurance company insures two types of vehicles, popular vehicles and vehicles luxurious. The damages claimed as a result of an accident involving a popular car have distribution N (7, 1) and the damages claimed as a result of an accident involving luxury has an N (20, 6) distribution. Suppose the company receives three accident claims of popular cars and a luxury car accident claim. Assuming that these four complaints are mutually independent, what is the likelihood that the total amount claimed for the three accidents involving popular cars exceeds the total claimed by the accident involving the luxury car?

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