If you ever took a statistics class you know that you should switch. But I used to get into this argument with my teacher all the time, where the actual probability is still 50/50 since you know going into it that you're going to remove one in the first place.

But the best way he explained it was instead of 3 let's say there are 100 shells. You choose one and then I'll remove 98 empty ones leaving only yours and one shell left. Would you switch then?

So as much of a problem as I had with the three shell scenario as presented, my stats teacher was one of the smartest people I knew, so I would switch every time.

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Posted by RB10

Member since Nov 2010

44286 posts

Posted on 3/22/24 at 8:15 am to CocomoLSU

The probability change is because going in you had a 66.6% chance of being wrong. By showing you one of the wrong choices, you now only have a 33.3% chance of being wrong. It’s not “removing” the wrong choice, it’s just showing you that it’s wrong.

33.3% chance of making the correct choice before -> 66.6% chance of making the correct choice after.

This post was edited on 3/22/24 at 8:19 am

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Posted by CockHolliday

Columbia, SC

Member since Dec 2012

4530 posts

Posted on 3/23/24 at 10:59 pm to CocomoLSU

quote:
But the best way he explained it was instead of 3 let's say there are 100 shells. You choose one and then I'll remove 98 empty ones leaving only yours and one shell left. Would you switch then?

This is how the answer was made clear to me as well. If there were 100 shells before me and I picked one, and the host with the knowledge of which shell had the money flipped over 98 empty ones, leaving only my shell and the last one...what are the chances that the shell I originally picked actually has the money? It's not 50%, it's 1%.

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