Question

The baseball World Series is won by the first team to win four games. Suppose both teams are equally likely to win each game. What is the probability that the team that wins the first game will win the series?

Answer 1

Since the first team to win four games is the winner, so this means that the World Series must consist of 7 games only.

Next assume that the team A wins the first match. In order for team A to win the series over team B, it must win at least 3 games out of the next 6.

Let X denote the number of games won by the team A in the next 6 matches.

Now,

P(team A wins) = 1 - P(team A loses)

Also,

P(team A loses) = P(X=0) + P(X=1) + P(X=2)

Now.

P(X=0) = ⁶C₀*(0.5^0)*(0.5^(6-0)) = 0.0156

P(X=1) = ⁶C₁*(0.5^1)*(0.5^(6-1)) = 0.0938

P(X=2) = ⁶C₂*(0.5^2)*(0.5^(6-2)) = 0.234

So,

P(team A loses) = 0.0156 + 0.0938 + 0.234 = 0.3434

So,

P(team A wins) = 1 - 0.3434 = 0.6566