Thread by @SarangSood

The Monty hall problem (A Probability Puzzle)

You’re on a game show. There are 3 doors & there’s a car behind one of the doors, while others are empty. You are asked to choose, so you go with door 1. The host instead opens a different door 2, but there's no car behind it. (1/n)

Now he offers you a choice: You can switch to door 3 or stay with your original decision of door 1. Which according to you has more probability of having the car?

There are two doors left and one car. It should be a 50-50 chance no matter which door you pick. But Wrong. (2/n)

From the beginning, you only had a 1 in 3 chance of picking the right door. When the host reveals one of the doors, it doesn't actually change the odds that you initially picked. The first choice remains a 1 in 3 shot. (3/n)

However, after one of the doors is revealed, you have a lot more information than the initial 1 in 3 random choice.

You now have a choice between the "one-of-three" door you chose originally or the "two-of-three" remaining doors you initially knew nothing about. (4/n)

That is a choice between sticking with your 1/3 chance or going with a 2/3 chance. And, as you know that the car is not behind that other 1/3 door (which the host opened), then the car must be more likely to be behind the other door you didn't pick. (5/n)

So you must switch to get a 2/3 chance of selecting the car.

This puzzle helps us to realise how with increase in information (like opening of the door 2) can challenge our decisions based on probability. People are bombarded with ever changing information everyday. (6/n)