Dean Ventures interview questions

I had a campus interview lasting 30 mins. There were a few warm up questions, the toughest being "Why do you want to join us after doing a Phd?" There were two probability or brainteaser questions, of which I remember only one: There are 2 red and 2 blue balls. I pick balls one by one without replacement. Before I pick each ball, I can make a guess and if I guess correctly, I get $1. No penalty for guessing wrongly. What is the expected value of the game? You can answer by working out from the case (R,B) = (0,0). This can be reached from (R,B)= (0,1) or (1,0), which will both give you $1,.. and so on.

Interview consisted just of two brainteasers. First question was: You have new neighbors next door, and you know they have two children. You see one of them playing outside, and it is a girl. What's the chance that the other child is also a girl? I said 1/2, but the interviewer said it's 1/3, which is clearly wrong. (If the prior information were simply that at least 1 out of their two children were a girl, then 1/3 would be correct). It seemed ridiculous for them to not know the answer to their own question, especially such a simple one.