cool logic problems

Cody

Random Quote Generator
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Gastown
I've run accross a few of these over the years, and once they are explained to me they make sense, but I rarely get them right initially....

who knows the answer to this one

Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you: 'Do you want to pick door #2?' Is it to your advantage to switch your choice of doors?


and yes, the airplane takes off ;)
 
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ChestonScout

opinions are like Jeeps..
Location
Clinton, Ut
depends on where you live in the world.....some places goats are much more desireable than cars..


But your chances are the same either door you choose


Unless Im a retard (most likely)
 
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EROK81?

Sell out
Location
SLC
Yes it is an advantage to switch doors at that point.

Why? I can't remember, I only know the answer. Too bad I don't, other I'd sound pretty smart. :rofl:

It actually ups your chances by quite if I remember correctly.

ChestonScout is clearly retarded.

Oh I think I got it.

Originally you have a 33% chance of picking the correct door with the car. So picking the first time gives you a 33% chance of getting the car.

Once one incorrect door is opened there are now two doors left. Now one door you know is wrong and only have two remaining choices. Which gives you a 66% chance of winning. (original 33% percent chance plus the incorrect 33%)

I think...
 
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Cody

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Gastown
how about this one....

A shopkeeper says she has two new baby beagles to show you, but she doesn't know whether they're male, female, or a pair. You tell her that you want only a male, and she telephones the fellow who's giving them a bath. "Is at least one a male?" she asks him. "Yes!" she informs you with a smile. What is the probability that the other one is a male?
 

Bart

Registered User
Location
Arm Utah
Yes, you switch doors, because now there's a 60% chance that that door is the right door. That was on the show 21.
 

Cody

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Supporting Member
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Gastown
Yes, you switch doors, because now there's a 60% chance that that door is the right door. That was on the show 21.

it's 2/3 technically ;) But, why is it 2/3 professor? Knowing the answer isn't enough!!!

I think it was on the show 21, but the paradox that both of these problems are variants of was first published in the late 1800's....or just slightly before the movie ;)
 

SAMI

Formerly Beardy McGee
Location
SLC, UT
That was on the show 21.

Exactly what I was thinking.. You just went from 33.33% chance of choosing the car to the two choices... If the host suggests a door, they're probably leading you to the other goat anyways.. . It changes everything
 
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EROK81?

Sell out
Location
SLC
it's 2/3 technically ;) But, why is it 2/3 professor?

I think it was on the show 21, but the paradox that both of these problems are variants of was first published in the late 1800's....or just slightly before the movie ;)

I learned my answer on NUMB3RS. :rofl:
 

Cody

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Gastown
the key to the first one lies in the host knowing what is behind each door. If the host is picking at random, it's a totally different equation.
 

TJDukit

I.Y.A.A.Y.A.S.
Location
Clearfield
The way I see it, as I see it with anything like gambling. You have a 50/50 chance either you are going to win or you aren't it's that simple. Granted I usually don't win but it doesn't change that fact that there are only two outcomes.
 

Cody

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Location
Gastown
If it were at random, then yes it would be 50/50. But the question states the host knows the location, so it becomes variable probability.

So, if you choose door one, you have 1/3 chance it's your door, and a 2/3 choice it's one of the others. The host eliminates one of the other doors, and you know the host didn't pick a door at random, then the odds are 2/3 for door #2 and 1/3 for door #1 at that point.

as for the dog gender one...same logic. Think about throwing a 2, 2 sided doggie-die. There are only 4 possible outcomes: MM, FF, MF, FM

if you know at least one of them is a mail, you can eliminate FF. You now have MM, MF, FM of which 2/3 of the possibility is for F. So, it's 1/3 that it's a male and 2/3 for a female.

If the question was "if the older one is a male, then what are the odds the younger one is a male" then it would imply specific order to the equation, in which case the odds would be 50/50 because they are independent probabilities.

restated this way is fun to mess with people too.

Say that a woman and a man (who are unrelated) each has two children. We know that at least one of the woman's children is a boy and that the man's oldest child is a boy. Explain why the chances that the woman has two boys do not equal the chances that the man has two boys?

For the reason stated above, the woman's odds are 1/3 and the man's are 1/2
 
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TJDukit

I.Y.A.A.Y.A.S.
Location
Clearfield
I'm not saying that those are the actual odds of winning, i know that it is now a 66% chance. In my view thats how I always look at things like that, it's not based on anything mathematical or logical really.
 

Spork

Tin Foil Hat Equipped
If it were at random, then yes it would be 50/50. But the question states the host knows the location, so it becomes variable probability.

So, if you choose door one, you have 1/3 chance it's your door, and a 2/3 choice it's one of the others. The host eliminates one of the other doors, and you know the host didn't pick a door at random, then the odds are 2/3 for door #2 and 1/3 for door #1 at that point.

So what happens if the host doesn't want you to win. :spork:
 
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