## Nov 18, 2009

### Monty Hall problem a.k.a. The 3 door problem

Although I'm sure most of the ToughNut readers are familiar with this problem but I've met a lot of people with great aptitude who seem to have all sorts of confusion and disagree with the solution. Lets discuss and debate about the conflicting opinions that we all have. Here it goes...

Monty Hall problem
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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. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?

1. I think I should not change my decision because it may be monty's secret game to confuse me,,

2. According to probability, the chances for choosing the other door is more than the selected before.

Chances of other door will shift to 2/3 and door selected before will have 1/3.

3. yo vidrohee.....bravo...the superiority of your mind is unsurpassed.....from down here, us "normal" folks can't even begin to imagine the height of ur "intellect" (read, stupidity)

4. ya.kanav is right.this is a famous problem indeed.this problem is even in the movie "21".

5. don't rely on probability even einstein didn't
just give some money to monty and ask him the solution...it does work in INDIA for sure

6. just give some money to monty and ask him the solution...it does work in INDIA for sure

If you give money, make it equal to the cost of the goat.

7. it is advantageous to change the decision. if you choose one of the goats among the three doors, the probability of choosing it is 2/3. so, the probability that you choose the wrong (goat) door is more. therefore, it s better to change your choice.

8. In this case the correct choice is to change which door you have picked.

The secret is that Monty has given up vital information in revealing which door has a goat behind it.