The Monty Hall Problem

You’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say Door 1, and the host, who knows what’s behind the doors, opens another door, say Door 3, which has a goat. He then asks you if you want to switch to Door 2. Is it to your advantage to switch your choice?

Answer: Yes, it is to your advantage to switch. When you first choose a door, you have a 1/3 chance of picking the car. The host will always reveal a goat behind one of the remaining two doors. By switching, you actually have a 2/3 chance of winning the car, as opposed to sticking with your initial choice, which remains a 1/3 chance.