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# Monty Hall Problem

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Monty Hall Problem: should we switch and why?

Guest Feb 28, 2015

#1
+17711
+5

You should switch.

When the game starts, you get to choose one door, so you have a 1 in three chance to get the right door.

When the game starts, the host gets the other two doors, so he has a 2 in three chance of getting the right door.

Would you then trade your one door for his two doors? I would.

This is what the host is offering you: his 2 out of 3 chance of winning versus your 1 out of 3 chance of winning.

Because he shows you a losing door doesn't change the odds (he always has to have at least one losing door).

If you keep your first door, you have a one-in-three chance of winning; if you switch, you'll win (on average) two out of three times.

geno3141  Feb 28, 2015
Sort:

#1
+17711
+5

You should switch.

When the game starts, you get to choose one door, so you have a 1 in three chance to get the right door.

When the game starts, the host gets the other two doors, so he has a 2 in three chance of getting the right door.

Would you then trade your one door for his two doors? I would.

This is what the host is offering you: his 2 out of 3 chance of winning versus your 1 out of 3 chance of winning.

Because he shows you a losing door doesn't change the odds (he always has to have at least one losing door).

If you keep your first door, you have a one-in-three chance of winning; if you switch, you'll win (on average) two out of three times.

geno3141  Feb 28, 2015

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