Current location - Training Enrollment Network - Mathematics courses - Mathematics problems of science in senior two.
Mathematics problems of science in senior two.
In this kind of challenge, let the number symbol "1" represent a team member to win, and the number symbol "2" represents a team member to win.

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.