There are two possibilities when you pick door 1: either you've picked a door with the prize behind it (33%) or you've picked a door with a goat behind it (67%)

There are two possibilities when you pick door 1: either you've picked a door with the prize behind it (33%) or you've picked a door with a goat behind it (67%). Assume you stick. In that case, you have a 33% chance you've picked the right door, as before. Opening another door doesn't change whether you've picked the right door or not originally. Assume you switch. In the case you've picked a door with a goat originally (67%), you will necessarily switch to the door with the prize. In the case you've picked a door with the car originally (33%), you will necessarily switch to a door with a goat. Therefore switching gives you a 67% chance of picking the door with the prize. Another interesting strategy to consider is "randomize" - what if you picked randomly between the two remaining doors? Then you'd have a 50% of getting the prize, since you're selecting randomly between two doors, one of which you know contains the prize.