When three friends go for a coffee, they decide who will pay the check by each flipping a coin and then letting the "odd person" (i.e., the person who has a different outcome) pay. If all three flips produce the same result (so that there is no odd person), then they make a second round of flips, and they continue to do so until there is an odd person. (a) What is the probability that exactly 3 rounds of flips are made? ( (b) What is the probability that more than 4 rounds are needed? ( (c) What is the expected number of coin flips?

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