Question

Mark and Erik are to play a tennis tournament. The first person to win two

games in a row or who wins a total of three games wins the tournament. Find

the number of ways the tournament can occur.

Answer 1

Let $M$ represent that Marck has won a game and $E$ represent Erich has won a game.

Sample space

$$S=\{MM, MEMM, MEMEM, MEMEE,$$

$$MEE,EMM, EMEMM, EMEME,$$

$$EMEE, EE\}$$

It takes no more 5 games to determine a winner.