# Probability

A group of n people meet at lunch for a cup of coffee. They play a game to see who gets to pay for all the coffees. Each person flips a coin. If all the coins come up the same except for one person, then that one person gets to pay for all the coffee. If the coins do not result in this way, then everyone flips again until there is exactly one person different. Obviously, the game doesn't work for less than three people. Also, as n grows large it may take many flips to decide the loser of the game.

(a) For n = 3 people, how many flips will it take on average to find a winner?

(b) For n = 10 people, how many flips will it take on average to find a winner?

(c) Find a general formula that computes the average number of flips as a function of n. Create a graph for n = 3...20 showing the number of required flips.

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#### Solution Summary

This solution is comprised of detailed explanation and step-by-step calculation of the given problems and provides students with a clear perspective of the underlying concepts.