# Mystery Box

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You have 3 boxes. One has a great prize in it and the other 2 are bad ones. You pick a box at random, but you don't know if it is the prize. You are shown the content of another box that is a bad prize. One unopened box remains. Do you keep your original selection, or change to the unopened box? Does it make a difference?

answered Apr 24 by (44,990 points)
original
answered Jul 21, 2014 by (425,400 points)

i would rather keep the original box i have

answered Mar 23, 2013 by (720 points)

You want to always switch the box. When you first pick the box, you had a 2 out 3 chance of losing (1 prize and 2 bad prizes). Your odds of winning are 1 in 3 or 33.33%. If you don't change your answer, this number can't change since the order of what is in the boxes does not change over time. However, If you switch boxes, your chance of losing is different. You now know which which box has one of the bad prizes, since it was shown to you, so you do not pick it (not allowed actually). There can only be one unknown bad prize remaining. The situation can now look like:

There are no other combinations.

You can go over each situation. Lets say you always pick the first column.
For A
Picked bad, 2 shown to you. You switch and win.

For B
Picked bad, 3 shown to you. You switch and win.

For C
Picked prize. 2 or 3 shown to you. You switch and lose.

So you win 2/3 or 66.65% of the time. You can repeat this with each door as your selection and the match is the same.

If you don't switch the odds are only 33.33%, but if you switch it jumps to 66.67%.  It defies common sense, but the math works out. When you are given more info, like which box has one of the bad prizes, it changes the odds..

answered Mar 23, 2013 by (4,000 points)

I think it doesn't really matter but I personally would keep the original because I think that one is special!!!!!

answered Mar 23, 2013 by (33,010 points)
Stay with your first one because i am always told your first instinct is your best also you have a 50 50 chance!
commented Mar 26, 2013 by anonymous
Actually, you don't have a 50 50 chance. The probability is 66-33 chance.
commented Jun 19, 2013 by (33,010 points)
How would that equal out because 66+33=99 and it needs to be 100
commented Sep 29, 2013 by (5,410 points)
66% and 33% are the percentage form of 2/3 and 1/3, respectively. You have three boxes, so that's how it adds up to 100%.

66% is actually .66666666666666666 (and on and on), so the lost 1% is in the repeating number.

...I think.
answered Mar 22, 2013 by (18,170 points)
To me, I would just live with what I've got, because I've experienced that if you backtrack your decision, you fall in the ditch....

- CraftyGirlJuJu