The Monty Hall Puzzle, A Game of Strategy, Not Luck
IIM Interview Question -
"You're on a game show and there are three doors. Behind one door is a car, behind the other two doors are goats. You can only choose one door. You pick a door, but before you open it, the game show host opens another door revealing a goat. He asks if you want to switch your choice to the other door. Will you Switch? Why?"
At first glance, it seems like you have even odds by just picking between the two doors. One has a car behind it, the other a goat, right?
The reality turns out to be counterintuitive.
Here is the Answer to the Monty Hall Puzzle
Let's look at it this way:
When you first pick a door, the probability the car is behind that door is 1/3.
That means the probability that it is behind one of the other two doors is 2/3.
Now, when the host—who knows what is behind the three doors—chooses one of the other doors and opens it to show you a goat, this does not change the original probabilities.
But here is the trick:
The probability that the car is behind your original door remains 1/3.
The probability that the car was behind one of the other doors (which is 2/3) now gets "concentrated" onto the only other unopened door because the host has eliminated one goat.
| Your Initial Pick | Host Opens | Car Behind | If You Switch | Result |
|---|---|---|---|---|
| Car | Goat | Your Door | Goat | You Lose |
| Goat | Goat | Other Door | Car | You Win |
So whichever door you switch to, you will have a 2/3 chance to win a car.
The final Answer is - Yes, You Should Always Switch.
Why Do IIMs Ask This in Interviews?
This puzzle will test:
- Your logical reasoning
- Your comfort with counterintuitive reasoning
- Your understanding of probability
- Your ability to make a decision when information is uncertain
It's not about giving a right or wrong answer. More importantly, it is about how you think, how you explain, and how you manage stress!