The Monty Hall Problem Explained: Should You Stay or Switch?

Imagine you’re standing in front of three closed doors.

Behind one door is a brand-new car.

Behind the other two doors are goats.

You choose Door 1.

The host, who knows what is behind every door, opens Door 3 and shows you a goat.

Now he gives you a choice:

Do you stay with Door 1, or switch to Door 2?

At first, the answer seems obvious: there are two doors left, so surely each one has a 50% chance of hiding the car.

But that is where this famous math problem becomes surprisingly difficult.

The mathematically correct answer is to switch.

And the reason comes down to probability.

What Was the Probability When You First Chose?

When you selected Door 1 at the beginning, you had a 1-in-3 chance of choosing the car.

That means there was a 2-in-3 chance that the car was behind one of the other two doors.