A certain sports league has ten teams in its Western Conference and

Probability that a team from Texas in the Western Conference reaches the Big Game, say P(TW) = 2/10 = 1/5
Probability that a team not from Texas in the Western Conference reaches the Big Game, (1-P(TW)) =1 - 2/10 = 8/10 = 4/5

Similarly,
Probability that a team from Texas in the Eastern Conference reaches the Big Game, P(TE) = 2/8= 1/4
Probability that a team not from Texas in the Western Conference reaches the Big Game, (1-P(TE) =1 - 2/8 = 6/8 = 3/4

If only one of the teams from Texas plays the Big Game, then the probability that the team from Texas win in that game is 1/2
If both teams in the Big Game are from Texas, we are not concerned about the outcome of the Big Game

Now, the probability that a team from Texas wins = P(TW)*(1-P(TE))*(1/2)+(1-P(TW))*P(TE)*(1/2)+P(TW)*P(TE)[/m]

\(=\frac{1}{5}*\frac{3}{4}*\frac{1}{2} + \frac{4}{5}*\frac{1}{4}*\frac{1}{2} + \frac{1}{5}*\frac{1}{4} = \frac{9}{40}\)

Answer is (C)

Hit Kudos if this helped!

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.