For the second part you pick a car after your friend picks a goat.

              FRIEND
 P[Car] = 1/3        P[Goat]=2/3
                        YOU
             P[Car]=1/2     P[Goat]=1/2

Use this as a binary transmission system, so P[Car|Friend chooses Goat] = (2/3)(1/2) = 1/3

Alumni Liaison

Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett