In a game called 'odd man out' , m (m > 2) persons toss a coin to determine who will buy refreshments for theentire group. A person who gets an outcome different from that of the rest of the members of the group iscalled 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 case s 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=mThus, the number of favorable ways is m + m - 2m. Therefore, P(A)=2m2m=m2m−1