In a game called "odd man out" m(m > 2) persons toss a coin to determine who will buy refreshments for the entire group. A person who gets an outcome different from that of the rest of the members of the group is called the odd man out. The probability that there is a loser in any game is

Let A denote the event that there is an odd man out in a game. The total number of possible cases is 2m. A person is odd man out if he is alone in getting a head or a tail.The number of ways in which there is exactly one tail (head) and the rest are heads (tails) is mC1=m. Thus, the number of favorable ways is m + m = 2m. Therefore,P(A)=2m2m=m2m−1