7 Puzzles And Paradoxes To Twist Your Brain
3. The Monty Hall Problem
What is it?
Here's a logic puzzle to put to your friends if you ever want to take them down a peg or two.
The Monty Hall problem is a counter-intuitive statistics puzzle, based on the popular game show, Let’s Make A Deal. It first became famous back in 1990, when a reader of Parade magazine sent it into Marilyn vos Savant's "Ask Marilyn" column for her to solve, which she did. This prompted a storm of letters from over 10,000 readers, many of whom had PhDs, angrily disagreeing with her solution, but she was right and they were wrong.
It goes like this:
There are 3 doors, behind which are two goats and a car.
You pick a door, door A for the sake of argument. You’re hoping for the car (although goats are cool.)
The game show host, Monty Hall, can see behind the other doors (B & C) and will choose one to open, he always opens one of them with a goat behind it (if both doors have goats, he’ll randomly pick one to open)
You are then given the option to either stick with your original door, or switch to the other remaining closed door
Which do you do? Do you stick with door A (your original guess) or switch to the other unopened door? Does it matter?
Fine. What's the solution?
Surprisingly, the odds aren’t 50/50 and you are much better off switching your door. If you switch, you’ll actually win two thirds of the time! It’s counter-intuitive as most people assume that two choices means a 50/50 chance. This is the mistake that Vos Savant’s enraged readers made, but look at it this way:
When you pick your door, you have a 1 in 3 chance of winning.
That must mean that the other doors have a 2 in 3 chance of having the car behind them.
Monty opens one of them to reveal a goat, which means that the 2 in 3 chance for the car is transferred to the one other remaining door. If you stick with your door, you only ever have a 1/3 chance of winning, which is still a chance. But if you switch, you are switching to a door that is more likely to hide a car.