Team A and Team B are both composed of three members, respectively. Each member is assigned with the order to play (e.g. first, second, and the last) and should obey the following rules. (a) The first players of Team A and Team B match against each other (b) The player who beat the opponent continues to play a game with the next player of the other team (c) If all members of any team are defeated, the game is over Find the probability that the second player of Team A wins only once. (The probability of each player winning is 0.5 and all matches end with a winner and a loser (there is no draw))
I think there are 5 cases of the second player winning. I just tried to count all the possible outcomes and got the answer to be 9/32. However i think i am wrong... Can anyone help me with this problem?