Question

The first player to win 2 sets is the winner of a tennis match. Suppose that whatever happened in the previous sets, each player has probability 1/3 of winning the next set. A)Determine the expected number of sets played.B)how about if now change to be first player to win 3 sets is the winner of a tennis match?

Answer 1

let x are the number of sets played

P(X=2)=P(first player wins first 2 sets)+P(second player wins first 2 sets)=(0.5*0.5)+(0.5*0.5)=0.50

P(X=3)=1-P(X=2)=1-0.5 =0.5

therefore expected number of sets played = $\sum$ xP(x)=0.5*2+0.5*3 =2.5