Two players contest a best-of-three match, so the first to win two games takes the match. Each game is won by Ishaan with probability 0.6, independently of the other games. What is the probability that Ishaan wins the match?

Ishaan takes the match either in two games or in three. Winning the first two has probability $0.6\times 0.6=0.36$. Winning in three games means losing exactly one of the first two and then taking the third: win-lose-win gives $0.6\times 0.4\times 0.6=0.144$ and lose-win-win gives $0.4\times 0.6\times 0.6=0.144$. Adding the three disjoint routes gives 0.36 + 0.144 + 0.144 = 0.648. The value 0.6 supposes the match mirrors a single game, but a longer contest favours the stronger player, which is exactly why 0.648 exceeds 0.6. The value $0.216=0.6^3$ is the probability of winning all three games, which is neither necessary nor sufficient for the match — the third game is never played once someone has won the first two. The value $0.936=1-0.4^3$ is the probability that Ishaan wins at LEAST one game.