How I Finally Understood the Famous Monty Hall Problem
Lessons I learned from the brain teaser that almost broke me
Imagine you are the contestant on a game show. There are three doors that you can choose from. Behind two of them are goats. Behind one is a new car.
Setting aside the possibility that some people prefer goats to new cars (what you do in your private life is none of my business) the goal is to pick the right door — the one with the car. You choose door number one and Monty Hall, the game show host, opens a door. But instead of opening door #1, he opens #2. It’s a goat.
Now you must choose again. But Monty Hall gives you the option of sticking with door #1 or switching to door #3. What should you do?
Most people naturally assume that it makes no sense to switch (or that it doesn’t matter) because the odds are 50/50 that either door has the car.
But that assumption is wrong.
The reason is that the odds of picking the right door on the first try are 1 in 3. That means that there is a 2/3 probability that the car is behind one of the remaining doors. But once door #2 is eliminated, there is still a 2/3 probability that the door you didn’t pick is correct. And with #2 no longer a viable option, the probability that #3 has the car…
