C = car, G = goat. Column 1 = Door 1, etc. The car could be behind any of the three doors, hence the three rows showing each possibility. C G G G C G G G C

C = car, G = goat. Column 1 = Door 1, etc. The car could be behind any of the three doors, hence the three rows showing each possibility. C G G G C G G G C You choose a door, say Door 1. Monty opens another door with a goat behind it. C x G G C x G x C Now look at the grid. Staying in column 1 gives you the probability space C G G, a 1/3 chance of getting a car. Switching gives you C C G, a 2/3 chance of getting a car.