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There are a couple approaches I like: "Which of the three boxes do you choose?" "Box A." "Is the prize probably in Box A?" "No, it's probably in one of the
by beej71 4y ago
There are a couple approaches I like:
"Which of the three boxes do you choose?"
"Box A."
"Is the prize probably in Box A?"
"No, it's probably in one of the two other boxes."
"So it's probably not in Box A."
"Correct."
"Look: Box C doesn't contain the prize. Do you want to stay with Box A which probably doesn't have the prize, or switch to one of Box B or C, which probably does have the prize?"
"Well, since Box A probably doesn't have the prize, I should switch to Box B or C. But I know Box C doesn't contain the prize, so I'll switch to Box B, which probably does."
Another approach is to make a lot of boxes.
"Here are 100 boxes. Choose one that has the prize."
"I choose box 17, which probably doesn't have the prize."
"Now I'm going to open 98 more boxes and show you that none of them contain the prize. As you see, only box 68 remains closed (as well as your box 17). Do you wish to switch to box 68?"
"Hell yes!"
- firstlink 4y agoI think the 100 box explanation misses a subtlety in the problem. Conditional on those 98 boxes being empty, box 17 and box 68 are equally likely to have the prize. The key is that you have a large probability of backing the host into a corner as it were: forcing him to choose 98 of 98 openable boxes vs 98 of 99. This is where your large probably of winning comes from, but it's no clearer in the large (100-box) example than the small. Therefore I posit that the large example exploits a misunderstanding about the solution rather than elucidating it.