The Monty Hall Problem

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?" Would it be beneficial for you to switch your door ?

Please do not check the answer from any other source. Think about it on your own. It yields a surprising result but is easy to solve.

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
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Comments

You should switch the door.

Zi Song Yeoh - 8 years, 1 month ago

That's correct. Have you heard of this before or did you get it on your own?

rahul sahaty - 8 years, 1 month ago

Just evaluate all possibilities.

Zi Song Yeoh - 8 years, 1 month ago

Switching door is the better option as it increases winning chance by 66%...this problem can be solves using Bayes' Theorem...people usually commit mistake when they think that there is 50-50 chance of winning after one door is open.

Yash Maurya - 8 years, 1 month ago

I have seen this in the movie "21"! But I don't really understand it! :P

Revanth Chetluru - 8 years, 1 month ago

There is a very easy way of explaining it. You could send me an email at rahulsahaty@gmail.com for the explanation as posting it here would reveal the technique.

rahul sahaty - 8 years, 1 month ago

You can solve it using a simple flow chart

rahul sahaty - 8 years, 1 month ago

i do not agree with switching it or not. the probability of being right is 50%. the probability of both remaining doors when one of the door has been removed, the choice is between the remainder. just like in the game show '' who wants to be a millionaire,''. when you select 50-50 life line, even if you were thinking of an answer before, it doesnt matter, the choice is still between two answers

Ayodele Ajiboye - 5 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$