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Al, Betty, Charlie, and Diane are working at the math club table during freshmen move-in week….

Al, Betty, Charlie, and Diane are working at the math club table during freshmen move-in week. Their attention spans for doing the job are independent and have exponential distributions with means 1/2, 2/3, 1, and 2 hours. (Rates are 2, 3/2, 1, 1/2.) (a) What is the expected amount of time until only two people are left? (b, 15 points) What is the probability the last two left have the same sex, i.e., AC or BD?