Question

Two baseball teams engage in a playoff series in which the series is won by the first team to win 4 games. If each team is equally likely to win any game, what is the expected number of games played?

Answer 1

P(game is played for 4 games)=P(X=4)=P(first team wins first 4 games)+P(2nd team wins first 4 games)

=2*(0.5)⁴ =0.125

P(X=5)=P(first team wins 3 out of first 4 games and wins 5th game)+P(2nd team wins 3 out of first 4 games and wins 5th game)

=2*⁴C₃(0.5)⁴*(0.5)=0.25

P(X=6)=2*⁵C₃(0.5)⁴*(0.5)²=0.3125

P(X=7)=2*⁶C₃(0.5)⁴*(0.5)³=0.3125

hence Expected number of games played =E(X)=4*0.125+5*0.25+6*0.3125+7*0.3125=5.8125