# Monty Hall Problem

The Monty Hall problem states that:

“Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?”

Before reading further, you may just note down what is there in your mind(Spoiler Alert!! :D). The explanation given below involves only basic probability; And I have put down everything in the way I had understood the problem.

Basic inferences that can be made:

P(G) = 2/3

P(C) = 1/3

In the next step, after the host opens the door, where the goat is present, only two options are left for the player. One of which, the player had chosen.

Let’s assume that the player always changes his choice. Now there is a
possibility that the currently chosen door has a goat or a car behind it.

If it was a car behind it, you would surely opt to choose the next unopened
door(assumed) - the probablity is 1/3, i.e. the probability of choosing car.

Else if there was a goat behind and you choose the next door - the probability
is 2/3.

Thus it is highly probable that you could win a car if you opt to change your choice if some problem similar to the above is thrown at you!! :)