Question

Imagine that you're on a game show, and you're given the choice of a mystery prize behind one of three doors: Behind one door is a car; behind the other two doors are goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to stick with door No. 1 or switch to door No. 2?" What do you do? Would you stick with your original pick or switch? Would either choice give you a better chance to winning the car?

Answer 1

Answer:

Switching would be better.

Step-by-step explanation:

If you pick a door at random, you have a 33.33% chance to get the car, and a 66.67% chance that the car is in the other two doors, 33.33% in the other two doors. (Let's pick door 1 for this example)

Saying that door 2 has a goat means that door 2 has a 0% chance of having a car. Where did that 33.33% go to? It went to door 3. Hence, door 3 now has a 66.67% chance of having a car.

Therefore, you should swap.