Castleton Public Library discussion

A different way to think about the Monty Hall problem. I hold 3 playing cards in my hand, one with a picture of a car and 2 that each have a picture of a goat. I tell you to pick a card at random. After you do so, there is a 2/3 chance I still have the card with the picture of the car. I discard a card with a picture of a goat. You can keep your card or you can swap it for the one card I still hold. There is only a 1/3 chance you have the car, but there is a 2/3 chance I have the car. This is because there was a 2/3 chance I had the car after you picked a card at random, and if I did have the car, I must have retained it, because I discarded a goat. Therefore, you should swap your card for mine.