This problem can be divided into 4 parts
A: P[pick car initially] = 1/3
P[win car without swapping/you picked car initially] = 1/3
B: P[pick goat initially] = 2/3
P[win car without swapping/you picked goat initially] = 0
C: P[pick goat initially] = 2/3
P[win car after swapping/you picked goat initially] = 2/3
D: P[pick car initially] = 1/3
P[win car after swapping/you picked car initially] = 0
So P[win car without swapping] = 1/3 and P[win car after swapping] = 2/3.
