Jane Street

Hi, a friend of mine who interviewed with Jane Street just gave me some of the brainteasers they threw at him. I tried a few of them out, and was wondering if anyone here can help me out with the question below :

In world series (baseball) there are two teams, A and B. You know that each can win 50% of the time (1:1 odds). You also know how the game works, i.e. Whoever wins 4 games first wins. What is the probability of getting to game 7 (i.e. Each team wins 3 games)?

So far, here's what I have...
Each event in the sample space is either a win by A and a loss by B or the other way round, and the probablity of that is 0.5^2
The probablity of this happening until the 6th game is (0.5^2)^6 = 0.5^12

Have a first-round FT interview with this firm next week. Has anyone interviewed with them that can offer any advice on preparing or remember anything useful?