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What if in the original Monty Hall problem, the host does *not* show you what's behind one of the doors that weren't picked?
You pick door #1. But this time, without telling you what's behind one of the other two doors, the host only asks if you want to switch to another door. Given that you now don't know what's behind doors #2 or #3, do you still stand a 2/3s chance of winning if you switch?
@thedogandthecello saidOkay. But think of it this way:
It would still be 1/3rd if no info is given.
[youtube]/hXOjyv4d998?si=LjgGYcP8mj7EuJBB[/youtube]
With no information you have a 1/3 chance of being correct. That means your first choice has a 2/3 chance of being wrong.
Mathematically, don't you still sand a better chance of switching to a different door if offered?
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@vivify
No because you don't get any info so it's still 33 percent chance.
Once you get a little info it helps but in your scenario it's 1 out of 3 random pick.
I saw a documentary about some lady who showed the math involved when you get some info and I think she said what you're saying.
I'm not sure if I can find it.
1 edit
-Removed-Say instead of the 3 doors there were 100 doors. Whatever door you choose has a 1/100 percent chance of being the correct door with the prize.
Since your first choice out of 100 was most certainly wrong, any other choice, no matter how minimal, would stand a higher chance of being the correct door...right?
Shouldn't the same apply to to choosing 3 doors in the Monty Hall problem (minus information)?
-Removed-So going to back to choosing 3 doors: you have a 2/3rds chance that your initial pick was wrong.
So since your there's a higher probability of your first pick being wrong than correct, logically it would make sense to switch to a different door when given the option, even if you don't receive any additional information. Right?