Lesson 7

Problem. Teams A and B play a tournament until two wins (the winner is the one who first wins two games; there are no draws). Team A wins the first game with probability \(1/2\). The results of Team A in each subsequent game depend on its result in the previous game: if Team A won the previous game, then, encouraged by the victory, it wins the current game with probability \(2/3\); however, if Team A lost the previous game, then, disappointed by the loss, it wins the current game with probability only \(1/3\). What is the probability that Team A will win the tournament, given that it won the first game?