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Pick a box! (Posted on 2002-03-28) Difficulty: 3 of 5
You are shown three boxes, and told that one of them contains a prize. You are then asked to pick one box, and if that box is the one with the prize, you will win it. After picking a box, you are shown that one of the other two boxes is empty, and offered a chance to change your selection.

Should you do this? Would changing your choice to the other remaining box affect your odds of winning? Why or why not?

See The Solution Submitted by levik    
Rating: 4.2857 (14 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): YES! ~33/66! All possibilites shown! | Comment 25 of 40 |
(In reply to re: NO! 50/50! All possibilites shown! by jduval)

p P S W          p P S W
1 1 2 N*0.5    1 1 2 Y*0.5
1 1 3 N*0.5    1 1 3 Y*0.5
1 2 3 Y           1 2 3 N
1 3 2 Y           1 3 2 N

Again p= box picked, P = box with prize, S = box shown, W = prize won?

 33%/66%

Ignore the host for a moment!  What are your chances of winning?  1/3!

You chances of losing?  2/3!

If you guess correctly in the beginning, it doesn't matter what the host does, you should stay!

If you guess incorrectly in the beginning, it doesn't matter what the host does, you should switch!

Since you are wrong 2/3 times, you should switch!

IT'S NOT FUN READING SOMTHING WITH LOTS OF CAPITAL LETTERS AND EXCLAMATION POINTS, IS IT?!?!?

Edited on March 1, 2005, 5:42 pm
  Posted by Dustin on 2005-03-01 17:42:05

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