please help me solve this

Question

h) Suppose Marck (M) and Erick (E) are playing a tennis tournament such that 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 proceed

Answer 1

Salim,

A simple decision tree is the easiest way to work through this, but it is nearly impossible to draw one in this editor. I'll try to lay it out for you without the lines. The lower case letters will indicate the winner of the individual game. Upper case letters will indicate the winner of the tournament.

 

 

              m                                     e

           /       \                             /         \

       M            e                      E                 m

                   /     \                                  /        \

               m          E                           e               M

            /      \                                /       \

         M          e                           E            m

                  /      \                                   /      \

                M          E                            E            M

 

Hopefully, you can see the possible progressions:

 

mM                                                      eE

memM                                                  emeE

meE                                                     emM

memeM                                                ememE

memeE                                                ememM

 

Ten possible progressions.