We recorded the winning or losing order of each match according to the sequence of matches, such as 1, 1, 2,2, 1, 2,2, 1, 1. That is to say, after 9 matches, No.5 of Team A finally won the match.
Obviously, team A and team B have the same chance of winning, so we assume that team A wins the game, so there will be five "1" and 0~4 "2" in the game record, and "2" can't appear at the end, so all possible situations are as follows:
0 "2": 1 species
1 "2": c (5, 1) = 5 species.
Two "2": c (5,1)+c (5,2) =15.
Three "2": c (51)+c (5,2 2) * 2+C (5 5,3) = 35 kinds.
Four "2": c (51)+c (5,2) * 3+c (5,3) * 3+c (5,4) = 70 kinds.
So there are 126 possibilities for team A to win, and there are 252 possibilities.
If Team A's No.5 finally wins the game, then Team A's No.65438 +0 to No.4 all lose, that is, there are four "2s" in 70 situations.
Therefore, the probability that Team A's No.5 will win the game is 70/252=5/ 18.