The Theory of Variable Change

A theory which is believed to be discovered by Newton & has been used to solve one of the most remarkable & controversial problem popularly known as the Monty Hall problem.

The statement as published in parade magazine :

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?

Now the thinking procedure of a common man at first sight would be to judge the motive the host, he would certainly sense that the chances of him winning a car is 1/2 & the host is trying to influence his supposedly correct decision by opening door No. 3.So he would opt to stick to his choice.

But a man who lets mathematic mingle with his common life would definitely switch to increase chances of letting his ass sit on a brand new car.Let's see why?

The man, having chosen a door, has a 1/3 chance of having the car behind the chosen door and a 2/3 chance that it's behind one of the other doors. It is assumed that when the host opens a door to reveal a goat, this action does not give the player any new information about what is behind the door he has chosen, so the probability of there being a car behind a different door remains 2/3; therefore the probability of a car behind the remaining door must be 2/3 Switching doors thus wins the car with a probability of 2/3, so the player should always switch.

Let us see another version of the problem

Monty Hall forgets which door hides the car. He opens one of the doors at random and is relieved when a goat is revealed. Asked whether the contestant should switch, no is the answer

"If the host is clueless, it makes no difference whether you stay or switch. If he knows, switch"