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reinout-g

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Usernamereinout-g
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 #6
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Melody:

Hard one (quite famous actually):

You are on a tv-show where you can win a million dollars. The flamboyant host asks you to pick one of three boxes.
In two boxes you will find nothing, but one box will give you a million dollars.
You pick a box and the host then decides to play a trick with you.
Since he knows what is inside each box he opens one of the boxes that has nothing in it.
He then asks you the million dollar question.
Will you stick with the box you picked, or will you switch to the other box?

Should you stick with the bos you picked, should you switch or is it irrelevant what you do?
Explain why please
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Okay Reiner-g, so you are saying that the probability that you chose correctly in the first place is 1/3
But the probability that the other cup iscorrect is 1/2
therefore if you swap cups your chance of being correct increase from 1/3 to 1/2 (an increased chance of 1/6 = 16.6% ? )
No I am still not right. Where did the 66.6% come from



vestri amicus is correct,

Think of all the possibilities with their probability

box 1 - you have the million dollar box, 33%
box 2 - you have an empty box 33%
box 3 - you have an empty box 33%

Now there are three scenarios given that you switch

1) you have the million dollar box, the host removes box (2 or 3) and you switch to box 3 which gives you nothing

2) you have empty box 2, the host removes box 3 you switch and win a million dollars,

3) you have empty box 3, the host removes box 2 you switch and win a million dollars.

Note that all these scenarios have equal probability since you can have either box 1,2,3.

I also like the other explaination of vestri amicus thinking of the same problem with more boxes.

The problem is known as the monty hall problem ( http://en.wikipedia.org/wiki/Monty_Hall_problem )

The answer to the problem is very counterintuïve, which is also how it became so famous.
Feb 27, 2014