The quiz master explains: You are allowed to open one of three doors,
if you open the correct one you will find a chest with hundreds of diamonds.
Open one of the other two doors and you will get nothing!

Mike looks at the three doors, but they all look the same, there
is no hint as to which one is the correct one. Finally he says:
"I choose this door" and points to one of them.

The quiz master looks at him and replies: "today I am in a good
mood, and therefore I will now give you a hint: I will open
one of the two doors you did not chose, and will show
you that this is one of the wrong doors". He goes over
and opens one of the remaining doors and everyone can see
that there is nothing behind it.

He continues "Now I give you a second chance: you can either
go with the door you originally chose, or switch to the other
door that is still closed".

And the question to you:
Hint: If Mike plays the game correctly he can boost
the probability of a win to well over 50%!

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Basically when you first choose a door, it has 1/3 of probability of being the right one, and 2/3 of being the wrong one.

There will always be an unchosen and empty door to show, so the event of opening cannot affect probability of the choice made on the first place. The probability of the other two unchosen doors will though collapse on the unopened one, which has now probability 2/3 of being the right one, and 1/3 of being the wrong one.

If Mike changes the door, he has 66.(6)% probability of success, against 33.(3)% he has if he doesn't change.

bydjjeckon Mon Aug 23 17:23:10 2010