Five people have just won a $100 prize, and are deciding how to divide the $100 up
Chapter 4, Problem 77(choose chapter or problem)
Five people have just won a $100 prize, and are deciding how to divide the $100 up between them. Assume that whole dollars are used, not cents. Also, for example, giving $50 to the first person and $10 to the second is dierent from vice versa. (a) How many ways are there to divide up the $100, such that each gets at least $10? (b) Assume that the $100 is randomly divided up, with all of the possible allocations counted in (a) equally likely. Find the expected amount of money that the first person receives. (c) Let Aj be the event that the jth person receives more than the first person (for 2 j 5), when the $100 is randomly allocated as in (b). Are A2 and A3 independent?
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