The Monty Hall Problem
Guess what? Your intuition doesn’t always tell you the truth. There might be no better way to prove this than by looking at the the Monty Hall problem. It’s generally regarded as one of the strangest problems in mathematics, due to the fact that its solution seems counter-intuitive and paradoxical. But if you look at it carefully, you will see that the logic and math behind the solution is flawless, and proves that your intuition often leads you astray.
Here’s the scenario: you’re a contestant on a TV game show. You find yourself in front of three doors. Behind one of the doors is a brand new car. Behind each of the other two doors is a goat. You have to choose one of the doors and for whichever door you choose you will win what’s behind it. Let’s assume you want to win the car. At the moment, you have a 1/3 chance of correctly choosing the door that the car is behind. You decide on one of the doors and tell the game show host your choice. The host then opens one of the two doors that you didn’t choose, revealing a goat. You now have the option of a) staying with the door you chose, or b) switching to the other door. Here’s where the counter-intuitiveness, paradox, and your intuition leading you astray comes in: while it might appear that you now have a 1/2 chance of winning the car no matter what you do, your odds of winning are actually doubled by choosing the other door! Look at the image below to see how this works:
No matter what door you chose initially, by switching doors once you know where one of the goats are, you will have a 2/3 chance of winning the car. By staying with the door you chose, your odds of winning will be 1/3. Therefore, always remember to trust probability and not your intuition, or you might find yourself taking home a goat.