2. Two Go teams, Team A and Team B, each have 5 players who compete in a relay match according to a predetermined order. The No. 1 players of both teams start the match, and the loser is eliminated; then the No. 2 player of the losing team competes against the winner, and the loser is eliminated again. This continues until all players of one team are eliminated, at which point the other team is declared the winner. Assuming each player has equal strength. What is the probability that 4 players from Team A are eliminated and Team A eventually defeats Team B?
2. $\frac{5}{18}$.

Since a total of 9 players from both teams have been eliminated, the match must have lasted 9 rounds, and Player 5 of Team A must have defeated Player 5 of Team B, with their order being fixed. Additionally, the number of ways the 5 players from Team A can appear is $\mathrm{C}_{10}^{5}$, and the number of ways the first 4 players can be eliminated is $\mathrm{C}_{8}^{4}$. Therefore, the probability that 4 players from Team A are eliminated and they ultimately defeat Team B is
$$
P=\frac{\mathrm{C}_{8}^{4}}{\mathrm{C}_{10}^{5}}=\frac{70}{252}=\frac{5}{18} .
$$