Suppose n people, n ≥ 3, play "odd person out" to decide who will buy the next round of refreshments. The n people each flip a fair coin simultaneously. If all the coins but one come up the same, the person whose coin comes up different buys the refreshments. Otherwise, the people flip the coins again and continue until just one coin comes up different from all the others.
a) What is the probability that the odd person out is decided in just one coin flip?
b) What is the probability that the odd person out is decided with the kth flip?
c) What is the expected number of flips needed to decide odd person out with n people?