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 Originally Posted by givememyleg
you have to think of it in two separate parts.
1) 1 out of 3 boxes is $300. 2 out of 3 boxes is $0.
2) 1 out of 2 boxes is $300. 1 out of 2 boxes is $0.
if you have your choice between the two, obviously you would pick #2.
The first "coin toss" was three side, whereas the next one is two sided.
Also, if it helps, try replace 3 boxes with 300 boxes. Then go through the problem again:
- Choose 1 box out of 300
- Of the remaining 299 boxes, 298 boxes are revealed as $0
- Do you stick with your box (at 1/300) or pick the new box (at 1/2)?
Math is still wrong here. It's still a 3-side cointoss, but now two of them net you $300. You basically get to choose between your first choice, or 'both of the others'.
And in the example of 300 boxes, you go from 1/300 to 299/300 chance.
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