A TV show paradox

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?

Easy Math Editor

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Comments

Yes. Since the probability of choosing a goat in the first try is 2/3 , since the other goat will be revealed, behind the other door should be the car. This famous problem as far as i know is The Monty Hall Problem.

Alain Caesar Torre - 7 years, 9 months ago

Yes, famous Monty Hall Paradox Refer here: http://en.wikipedia.org/wiki/MontyHallparadox

Priyansh Sangule - 7 years, 9 months ago

Where the same article also says that the question as posed is incomplete (what if the host knows Door 2 has a goat and hence offering the option; never offering the option if the player originally picked a goat?). So there is no satisfying answer for this problem as stated. Only after clarifying further that the problem can be solved.

Ivan Koswara - 7 years, 9 months ago

Probability of finding a car in door 2 is 2/3 whereas in door 1 is 1/2 . Apply the theory of probability whenever options seems to be close

Rahul Nahata - 7 years, 9 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}`	$\boxed{123}$