Monty Hall Problem
Let's look at the Monty Hall problem. A pretty standard Probability problem. Let's look at the problem - The problem is inspired from the Game Show "Let's Make A Deal", hosted by Monty Hall, after whom the problem is named. The rules of the game are - You are given 3 doors, out of which behind 2 are a goat, and behind the third one, lies a car. You are to choose one of the 3 doors, then Mr Monty opens one of the remaining door behind which lies a goat. Now, you are given a choice to either maintain your choice, or to switch. Probabilistically, which is better given that you would want a car. Thinking casually would probably make you feel that both would probably give a 50-50 chance of winning a car, but mathematically, that is evidently not the case. Mathematically Thinking Let us say we have 3 doors, A, B and C. Say, we choose door A. P(Car ∈ A) = 1 ⁄ 3 P(Car ∈ B) = 1 ⁄ 3 P(Car ∈ C) = 1 ⁄ 3 Because we have 2 Goats and 1 Car behind t...