The best way to look at this part of the problem is to divide it into 3 events. A: [You-Car,Friend-Goat], B: [You-Goat,Friend-Car], C: [Both picked goats]. From there you can use the condition that your friend was kicked off. So, for event A, if you switch, P(winning) = 0. Not switching: P(winning) = 1. You can determine the probabilities of other events in the same fashion.
