A brain teasing probability puzzle
- Thread starter Neki
- Start date
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This entire thread was fucking stupid. A million words wasted when all you had to do was do the problem yourself.
DOOR #1 -(GOAT)
DOOR #2 -(GOAT)
DOOR #3 -(CAR)
Possible outcomes:
IF YOU PICKED DOOR #1 (THE GOAT) IN ROUND 1:
You pick door #1, host reveals door #2, youSWITCH, and youWIN.
You pick door #1, host reveals door #2, youSTAY, and youLOSE.
SWITCHINGis the right choice. (Switching 1, staying 0)
IF YOU PICKED DOOR #2 (THE OTHER GOAT) IN ROUND 1:
You pick door #2, host reveals door #1, youSWITCH, and youWIN.
You pick door #2, host reveals door #1, youSTAY, andLOSE.
SWITCHINGis the right choice. (Switching 2, staying 0)
IF YOU PICKED DOOR #3 (THE CAR) IN ROUND 1:
You pick door #3, host reveals either door #1 or door #2, youSTAYandWIN.
You pick door #3, host reveals either door #1 or door #2, youSWITCHandLOSE.
STAYINGis the right choice. (Switching 2, staying 1)
CONCLUSION: If you always switch, you will win twice as often than if you always stayed. No thought or over-complication required. Just work through the fucking possibilities.
DOOR #1 -(GOAT)
DOOR #2 -(GOAT)
DOOR #3 -(CAR)
Possible outcomes:
IF YOU PICKED DOOR #1 (THE GOAT) IN ROUND 1:
You pick door #1, host reveals door #2, youSWITCH, and youWIN.
You pick door #1, host reveals door #2, youSTAY, and youLOSE.
SWITCHINGis the right choice. (Switching 1, staying 0)
IF YOU PICKED DOOR #2 (THE OTHER GOAT) IN ROUND 1:
You pick door #2, host reveals door #1, youSWITCH, and youWIN.
You pick door #2, host reveals door #1, youSTAY, andLOSE.
SWITCHINGis the right choice. (Switching 2, staying 0)
IF YOU PICKED DOOR #3 (THE CAR) IN ROUND 1:
You pick door #3, host reveals either door #1 or door #2, youSTAYandWIN.
You pick door #3, host reveals either door #1 or door #2, youSWITCHandLOSE.
STAYINGis the right choice. (Switching 2, staying 1)
CONCLUSION: If you always switch, you will win twice as often than if you always stayed. No thought or over-complication required. Just work through the fucking possibilities.
Abefroman
Naxxramas 1.0 Raider
- 12,594
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Well good thing you cleared that up for us. I picked switching cause spacey. Fuck your math.
There was actually no math involved other than the ability to comprehend that 2 is > 1, so I'm not sure how this shit still eludes people like Araysar. It's only a "thought experiment" if all people did was sit there and thought about it. Just fucking go and experiment. All it takes is 5 minutes to run through the permutations yourself to test which is the better choice.
That's not proof; that's you word-vomiting. Run through the permutations and report back to me with your results.
BrutulTM
Good, bad, I'm the guy with the gun.
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I used to hate this kind of shit when we used to interview engineers for our department. There were always a couple guys that would ask technical or math questions as if their ability to recite things from memory or solve a brain teaser under duress was relevant to their future job performance. I really think they were mostly trying to make the poor guy look stupid so they could feel smart themselves. I always thought that it was way more important to try to find out about their personality and whether they would fit in with the other people in the department than to find out whether they can answer some obscure question off the top of their heads.
Dyvim
Bronze Knight of the Realm
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Yeah alway switch as Soy points out. Also in case of a zombie apocalypse make sure you are the first when drawing matchsticks, since your chanches are lowest then and the other dude will end up on the short end and will have to risk his life to pick up the shot gun on the other side of the street.
At first I was 33% certain that Araysar was trolling but now I've switched to being 66% certain. As I understand the problem that means there's 100% chance that Araysar is a goat. Now, where is my car?
Thank god you saved us from all that time wasted by saying the exact thing twelve others have already done..but with COLORS!
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I have to ask, are you willing to be convinced that you are wrong if a sufficient explanation is provided to you?
Or are you trolling/ to stubborn to change your mind if presented with a better understanding.
Because with complete honesty although I knew the Monty Hall problem and the statistical result it took me a long time to really wrap my head around it, and I think I can do one better to explain it for you if you're being legit here.
Loser Araysar
Chief Russia Reporter. Stock Pals CEO. Head of AI.
- 81,594
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1. I have never had a problem with admitting that I am wrong. Well, thats a lie - in my early 20s I did. In the last half a decade I am much more comfortable with admitting that I dont know things. If anything, I think the ability to admit that you're wrong is a fairly impressive character trait.
2. I have never trolled on these boards. Frankly, these accusations are tiresome and ludicrous.
Tanoomba
ジョーディーすれいやー
- 10,170
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Dude, the most hilarious part of all your claims is that simulating the problem (either using the provided simulator or doing it with a friend and 3 playing cards) somehow produces incorrect result because it "works from the wrong premise that the first choice matters". What the hell does this mean?You're simulating the problem exactly as it's worded. You getconclusiveresults. If you think the results are "wrong" somehow then, clearly,you'rethe one working from the wrong premise.
If you pick the door with the car and change, you lose. If you pick the door with a goat and change, you win. Those are the two possible outcomes if you choose to change. This is the binary choice. But it is NOT a 50/50 choice. There is a 1/3 chance that you will pick the door and change. So, a 1/3 chance that changing will lead to a loss. There is a 2/3 chance that you will pick a goat and change. So, a 2/3 chance that changing will lead to a win. This is how it works.
Yes, it's impossible to win after the first round. However, you still either chose the door with the car (less likely) or the door with a goat (more likely) first. Changing your choice literally reverses those odds. If you picked a goat (which was more likely), you get to switch to a car. If you picked the car (less likely), you switch to a goat. I don't know how this can be made any simpler.
Izo
Tranny Chaser
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Well let me give it a shot old sport.
Tell me where at which point you start to disagree with my logic:
1. The contestant has a 1/3 chance of picking the car.
2. Monty Hall has a 2/3 chance of being left with the car, after the contestant chooses.
3. The Contestant switches because Monty hall has a higher probability of having the car.
4. The confusion comes in the second round, because Monty Hall eliminates one of the Goat Boxes
5. You are making a binary decision in round two so its obvious andalmostalways correct assumption to say the decision is a 50/50, when making a binary decision.
6. However, in this instance you have more information on the boxes than you may be aware of, this information can be perceived of as a physical weight you attach to one of the boxes.
7. Let's go back to the first round where we agreed that choosing a box gave us a 1/3 chance of having the car and Monty Hall a 2/3 chance of having the car as a result of your pick.
8. The Contest only got one pick so we give him a 33 lbs weight, So now we give Monty Hall a 66 lbs weight, because he has two boxes.
- We interpret in this scenario that Monty Hall is not "picking" a box, but in fact he is, he's just picking the two left over boxes, basically Monty Hall gets two picks to your one.
- We don't apply any extra weight to the contestant for getting to go first because he never looked under his box and still has the chance to change his decision, it does not offer the contestant any greater probabilistic advantage to have picked first.
9. From [4.] this again where the confusion came in, this is where Monty Hall removes one of the Goat boxes.
- We've established from the Monty Hall question that Monty hall will only remove a goat box
- So Monty Hall removes a goat box, do we take away 16 lbs From Monty Hall's 66 lbs weight giving only 50lbs to his box?
10. No, we do not, the 66 lbs weight is one solid dumbell, this is because although one box was removed from the scenario, and although the choice we are now making is binary, we've
established from the weight (information) that Monty Hall had two chances to pick the box with the car.
-This means that Monty Hall was able to nitpick his choice, he has to get rid of a goat box, but it doesn't change the fact that he was more likely to have picked the car with the box than you.
- At this point it wouldn't matter had Monty Hall been told before hand which box had the car-assuming there is a car in one box-Monty was from both of his selections able to deduce which box that was.
11. The probability isn't based on the number of boxes Monty has left, it's based on the fact that Monty was able to pick two boxes, thus he was twice as likely as you to find the car box and by deduction knows for certain who has the box with the car.
12. Staying with your box means a 1/3 probability/a 33 lbs weight/ or 33% chance of getting the car, because you only got one pick. Switching to Monty's box will give you a 2/3 probability/ a 66 lbs weight/ or a 66% chance of picking the car because he got to pick twice. Although you are making a binary choice, the outcome of the first round gives you insight into the probability being higher that Monty's box is the box with the car.
