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?

(In reply to re: NO! 50/50! All possibilites shown! by Dustin)

I am sorry.  I still believe you are wrong.

There are 9 equally likely possibilities:

You pick box one, 1 has prize.  Host reveals box 2 or box 3 empty.  Either way, stay
You pick box one, 2 has prize.  Host reveals box 3 empty.  switch
You pick box one, 3 has prize.  Host reveals box 2 empty.  switch

No,  There are 12 equally likely possibilities

You pick box one, 1 has prize.  Host reveals box 2 empty.    stay                                                                                   You pick box one, 1 has prize.  Host reveals box 3 empty.     stay
You pick box one, 2 has prize.  Host reveals box 3 empty.  switch
You pick box one, 3 has prize.  Host reveals box 2 empty.  switch

Why did you list them together.  They are two separate occurences?

Again in your second example:

You pick box one, 1 has prize.  Host reveals box 2 empty.  stay
You pick box one, 1 has prize.  Host reveals box 3 empty.  stay
You pick box one, 2 has prize.  Host reveals box 3 empty.  switch
You pick box one, 2 has prize.  Host reveals box 3 empty.  switch
You pick box one, 3 has prize.  Host reveals box 2 empty.  switch
You pick box one, 3 has prize.  Host reveals box 2 empty.  switch

Also No,

You pick box one, 1 has prize.  Host reveals box 2 empty.  stay
You pick box one, 1 has prize.  Host reveals box 3 empty.  stay
You pick box one, 2 has prize.  Host reveals box 3 empty.  switch
You pick box one, 2 has prize.  Host reveals box 3 empty.  switch
You pick box one, 3 has prize.  Host reveals box 2 empty.  switch
You pick box one, 3 has prize.  Host reveals box 2 empty.  switch

You listed some examples twice, you can not list them twice.  The rules state the host can only reveal an empty box that you did not choose.  Eliminate the italic underlines from your example and you are left with 50/50. 

For simplicity I did not list all three cases again 

The rules eliminate 2 of the 6 possibilities above.  Dependent upon which box you choose and which box the prize is in there are only 4 possibilities for the host to show you.  If you are correct he can show you one of two boxes, if you are wrong he can only show you one other box.

You can make a separate chart with every single possibility, including showing the box you chose and showing the box with the prize, switching or not switching.  And you will see that the rules are what eliminate the other possibilities (yes=switch) and not switching the boxes as the solution would state.  I may post it if I need to.

Posted by john on 2005-03-02 21:03:49