Mathematics and Let's Make a Deal - What's Behind Door Number 1?

Suppose you had the chance to be on the famous 1970's game show "Let's Make a Deal" which was hosted by the genial and oft witty Monty Hall. You are given a choice of three doors to select from, behind one of which is a new car. You select door Number 1. The witty Monty Hall decides to open up door Number 2 to reveal a goat. He now gives the chance to switch your door selection. The question is do you switch or stay with your original selection? Well a knowledge of mathematics, and in particular variable change, tells you what to do.

Deal

For those of you reading and processing this, you may have said to yourself that you saw this problem appear in the recent movie release "21," starring Kevin Spacey and Jim Sturgess. Actually this is the famous Monty Hall problem presented to Ben, the character played by Jim Sturgess, by Professor Rosa, played by Kevin Spacey. Ben correctly solves the problem in the movie and as a result of having impressed his math professor, is enjoined to hitch to the secret MIT blackjack team. Now if you saw the movie, you know what Ben did: he switched doors (oh, and joined the blackjack team). But why?

This article is about Deal

Let's analyze this problem carefully and the reason will come to light. This is not obvious by the way and after reading this you still might be scratching your head as to why the switch should be made. If you think carefully though and reason through it, the motivation behind the switch will eventually become clear. So let's start cogitating.

Behind exactly one door is a brand new car. There are three doors. Behind the other two doors are hungry yet benign goats. The probability of selecting the door with the car is obviously 1/3, and the probability of selecting a goat is then 2/3. Now I put forth that the clever Ben Campbell in the movie was right to switch, explaining to his professor and classmates, that by virtue of the switch he increased his probability of landing the car to 2/3 from 1/3, courtesy of the benevolence of his professor. But why?

The easiest way to see this, I think, is as follows: the probability of selecting the right door is 1/3. The probability of losing is 2/3. You have selected door Number 1, which has a probability of 1/3 of having the car. You have a 2/3 chance that you do not have the car. When Monty Hall reveals the goat behind one of the other doors, he has essentially just transferred 1/3 of the probability to you if you make the switch, giving you now a 2/3 shot of getting the car.

How you say? Well separate the test into the door you select and the other two doors. The probability that the car is in one of those two doors is 2/3. You have been shown that one door does not have the car. By switching, you now have a 2/3 shot of getting the car because you now have one of the doors in the group with a 2/3 probability. That's all there is to it.

Yes, I know. You might be scratching your head thinking, "I don't get it." Just go back to the last paragraph and reread it a few times. Think about it. The answer will surely come. Math: Yes that's the real deal.

Mathematics and Let's Make a Deal - What's Behind Door Number 1? People search Deal and look in this page

Recommend : nose jobs before and after Five Star Hotels In Paris