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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. You pick a door, say No. 1, and

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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. 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?

Guest Jan 8, 2015

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Originally, the game show host has two doors and you have one.

Therefore, the game show host has a 2 to 1 advantage over you.

So, you want to switch with the host and then you will have the 2 to 1 advantage. (The fact that the host shows you a losing door does not change the odds; it just confuses the problem.)

If you keep your original door, you have a 1/3 probability of winning.

If you switch, you have a 2/3 probability of winning.

geno3141  Jan 8, 2015
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yes, because at first you only have a 33.3% chance of getting it right, but on the second attempt, you get a 58.3% of getting right

Guest Jan 8, 2015
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Originally, the game show host has two doors and you have one.

Therefore, the game show host has a 2 to 1 advantage over you.

So, you want to switch with the host and then you will have the 2 to 1 advantage. (The fact that the host shows you a losing door does not change the odds; it just confuses the problem.)

If you keep your original door, you have a 1/3 probability of winning.

If you switch, you have a 2/3 probability of winning.

geno3141  Jan 8, 2015
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This is a reapeating question but always a good one. :)

Melody  Jan 8, 2015
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Do you even get the question right? Because adding the odds that you will actually be able to open a box/door means a 1/100000000000000 chance that you'll even answer right. But let's just say that you somehow answered right. In the beginning, you have a 1/3 chance of winning. After the judge shows the empty box/door, you have a 1/2 chance. It's that simple. So geno3141 is WRONG!!!!

Guest Apr 22, 2015
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No anon, you are the one that is wrong

Melody  Apr 23, 2015