Question

The Monty Hall problem is a probability problem that has stumped even math Ph. D’s. Write a report about it, which includes a statement of the problem, its solution, and a brief description of its history, including who suggested the problem in the first place.

Answer 1

The Monty Hall problem

The problem is named after the presenter of a US game show who ran a competition in the format.

The game goes like this : Suppose you are on a game show, and you are given the choice of selecting 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?

Mostly people will believe that it does not matter, and they have a 50:50 chance of winning. However, amathematical analysis shows that sticking to the first choice of door has only a 33% chance of winning. So the other unopened door must have a 67% (100%-33%) chance of winning.

Probability of the grand prize behind the 1st door = 1/3.

Probability that your grand prize is NOT behind the 1st door=1– 1/3= 2/3= Probability of the grand prize behind the 2nd OR 3rd door.

The reason behind increasing of Probability of the grand prize behind the 2nd door is simply the elimination of the 3rd door since you know the fact that the 3rd door contains no prize.

Explantion :

The first door has exactly 1/3 chance of being right. It's a simple selection between three things.

Most of the people miss that, because Monty(The host) knows where the prize is, his opening of the second door gives no additional information whatsoever.

If the 1st guess is correct, he just randomly chooses one of the other doors, both of which contain goats.If, however, the first guess was wrong, he simple choose the door that contains the other goat.

So, What the second door is doing is just adding tension, not actually changing anything - we already knew there were two goats . showing a picture of one of them doesn't help in decison making.