@ImplyingImplications @alt_total_loser I think, probabilities are high, this includes those who confirm their proves.
Mostly the problem descriptions suffer from equivocation and unclear process frame. #babylonianLinguisticConfusion
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ImplyingImplications@lemmy.ca 9 months ago
Humans are bad at statistics and probability. We’re naturally wired to find patterns and connections and make decisions quickly without needing to perform calculations. It works for simple stuff but when things get a little complicated our “gut feeling” tends to be wrong.
My other favourite probability paradox is the Monty Hall Problem. You’re given the option to pick from 3 doors. Behind 2 of them are goats and behind 1 is a new car. You pick door #1. You’re asked if you’re sure or if you’d rather switch doors. Whether you stay or switch makes no difference. You have a 33% chance of winning either way. Then you’re told that behind door #2 there is a goat. Do you stay with door #1 or switch to door #3? Switching to door #3 improves your odds of winning to 66%. It’s a classic example of how additional information can be used to recalculate odds and it’s how things like card counting work.
dichotomiker@dresden.network 9 months ago
Iamdanno@lemmynsfw.com 9 months ago
After you find out there’s a goat behind door #2, you have a 50% chance whether you stay on 1 or move to three. There are only two possible outcomes at that point (car or goat), so either way it’s a coin flip.
Feathercrown@lemmy.world 9 months ago
You’re wrong, but you’re in good company. It’s a very counterintuitive effect. One technique that can be helpful for understanding probability problems is to take them to the extreme. Let’s increase the number of doors to 100. One has a car, 99 have goats. You choose a door, with a 1% chance of having picked the car. The host then opens 98 other doors, all of which have goats behind them. You now have a choice: the door you chose originally, with a 1% chance of a car… or the other door, with a 99% chance of a car.
june@lemmy.world 9 months ago
Oh that’s so weird. I get it from a proof perspective but it feels very wrong.
My brain tells me it’s two separate scenarios where the first choice was 99:1 and after eliminating 98 there’s a new equation that makes it 50:50.
Silentiea@lemm.ee 9 months ago
The important thing is that the host will always show you a goat, meaning the old way the other hours bed the car old if you kist so happened to pick it the first time.
Take the situation to the extreme and imagine a hundred doors, and after you pick a door, the host opens 98 doors, all of them with goats behind them. Now which seems more likely, that you chose right the first time, or that the other door has the car?
Feathercrown@lemmy.world 9 months ago
Yeah it’s very counterintuitive
Iamdanno@lemmynsfw.com 9 months ago
Now you have 2 choices: the door you chose, or the only other door left. One has a goat and one has a car. That’s fifty-fifty.
In your explanation, the door originally had a 1% chance, but after showing 98 goats, it has a 50% chance.
ta_leadran_orm@lemmy.world 9 months ago
I would have agreed with you a couple of weeks ago, but this video explains it well. It wouldn’t be such a well known fallacy if it wasn’t so counterintuitive.
youtu.be/ytfCdqWhmdg?si=bNplB3ftYAfvnLYO
Hellnikko@lemmy.world 9 months ago
You’re incorrect. It is indeed a higher chance to switch from #1 to #3. You should look up Monty Hall paradox. It’s in the link that you replied to that explains it.
DarkDarkHouse@lemmy.sdf.org 9 months ago
You can test it empirically. It’s clearly not 50%.
Iamdanno@lemmynsfw.com 9 months ago
There are only two options at that point. It MUST be 50-50.
DarkDarkHouse@lemmy.sdf.org 9 months ago
Not sure if sarcastic… but seriously play it yourself a few times. If you’re unsure, keep playing and it will become clear.
UndercoverUlrikHD@programming.dev 9 months ago
People will claim that you’re wrong, but you’re 100% correct. It’s always 50-50. You either win, or you don’t.
Silentiea@lemm.ee 9 months ago
The important thing is that the host will always show you a goat, meaning the only way the other door has another goat is if you just so happened to pick the car the first time.
Take the situation to the extreme and imagine a hundred doors, and after you pick a door, the host opens 98 doors, all of them with goats behind them. Now which seems more likely, that you chose right the first time, or that the other door has the car?
UndercoverUlrikHD@programming.dev 9 months ago
My comment is clearly sarcastic…