This thread needs an argument for the case where the host picks a door at random. The chance for the host getting the car is of course also 1/3. Then the compl

This thread needs an argument for the case where the host picks a door at random. The chance for the host getting the car is of course also 1/3. Then the complement 2/3 chance of the host getting a goat splits the car chance evenly between the two remaining doors as 1/3 for each door.