Monty picking randomly adds a third outcome. You then have a) Staying wins (Monty opens to a goat) b) Swap wins (Monty opens to a goat) c) First pick lost, n

Monty picking randomly adds a third outcome. You then have a) Staying wins (Monty opens to a goat) b) Swap wins (Monty opens to a goat) c) First pick lost, no chance to swap (Monty opens to the car) each of equal probability.