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/sci/ - Science & Math

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3357448 No.3357448 [Reply] [Original]

>talk to roommate
>discuss the Monty Hall problem
>he thinks it's a 50/50
>I explain mathematically that it isn't
>"yeah, i get it, but there's a difference between mathematical probability and practical probability. It's really a coin toss"
>mfw

>> No.3357455

oh wow, an idiot.

who cares

>> No.3357452
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3357452

>>3357448
>talk to roommate
>talk to human being IRL

>> No.3357480

Oh how I more and more hate the imperfections of the human, not being able to completely KNOW and therefore relying on bullshit systems like statistics..
Statistics is what is holding us all back, because we're relying on it so, so much. But then again, it's the only useful tool to analyze data that's otherwize unanalyzable. It's fucked up.l

>> No.3357486

I'm extra confused. how did he get 1/2?

I thought the traditional wrong answer was 1/3? and then it goes 2/3 if you switch?

>> No.3357490

This conversation probably never took place.

>> No.3357508

>>3357486
because you either win or lose, so its 1/2.

>> No.3357517

>>3357486
It's intuitively 50/50 because when the host opens the door, it feels like he's removing an option. In reality that option was never there to begin with, but because you see the number of closed doors go from three to two, you instinctively think it's changed the situation. 2 choices = 50/50 intuitively, though the setup of the problem makes that mathematically false.

>> No.3357523

>>3357508

When visiting 4chan you either get b& or not.
That's two different events. Therefore probability is 1/2

>> No.3357527

I still don't get why it's 2/3.
It's certainly not 1/2 and I know how it works but...can someone explain to me IN WORDS why the the probability doubles and does not stay the same?

>> No.3357540

>>3357527
http://www.youtube.com/watch?v=mhlc7peGlGg

>> No.3357537

>>3357527
read the wiki
the solution is 1 - chance of choosing correctly the first time.

>> No.3357541

>>3357527
If you always swap, the only way to lose is pick the correct door initially, with probability 1/3.

>> No.3357548

I'm sure your roommate's an idiot but he accidentally made a good point, which is that the answer depends on Monty's motivations for opening the door, which for practical purposes are unknowable. All that can be said with certainty is that the true probability is somewhere between 1/2 and 2/3.

>> No.3357551

>>3357527
You pick a door. The probability of being right is 1/3. Host removes door. Your choice is still 1/3. Therefor, the other door is 2/3 and a switch is beneficial.
If it's not intuitive, consider if there were a hundred doors. You pick one, and the host removes 98. Obviously you would switch, right?

>> No.3357553

>>3357527
you have a 1/3 chance of selecting the correct door at the outset, and a 2/3 chance that you selected incorrectly. When the hosts ask you if you want to switch, hes asking you if you think the car is behind one of the 2 doors you didn't pick, rather than the one that you did, so switching doubles your chances. switching means you're selecting two doors as possibilities instead of one. It doesn't matter whether he shows you a goat or not, he is obligated to give you the car if its behind one of the two you didn't pick and you switch.

>> No.3357556

>>3357548
Can you elaborate? Sounds interesting.

>> No.3357560

>>3357548
You sound as retarded as his roommate

>> No.3357562

>>3357553
The fuck? I dont think you even understand the problem. That was completely wrong.

>> No.3357572

>>3357548
No, it's part of the traditional problem statement that Monty eliminates a door which does not have the car behind it.

>> No.3357569

>>3357556
If he accidentally opened the door, then it's a 50-50 situation. So it all depends on his intentions. There's an interesting article on this: http://www.probability.ca/jeff/writing/montyfall.pdf

>> No.3357570

>>3357548
OP here. he's not an idiot, just not inclined toward math and science. He's a good logical thinker (i've lost my share of moral debates to him) and with enough explanation i'm sure he'd agree with the math.

>> No.3357578

>>3357569
If he opens the door before you choose, it's 50-50, yes.

>> No.3357579

Just draw him a fucking decision tree if that's what it takes

>> No.3357596

>>3357572
But if he did so accidentally, then it's 50-50. I'm not sure what traditional formulation you're referring to, but Monty's motivations are NOT specified in the original Marilyn vos Savant question that caused a big shitstorm. (They're hinted at, though.)

>> No.3357597

>>3357579
I did. His issue is that he thinks the margin of error factors into the probability. for instance, because the probability that you will get exactly 66 cars out of 99 tries with switches is low, then the 1/3 probability is false. Again, he doesn't have much experience with statistics.

>> No.3357599

>>3357527
look at all the options:
You pick a random door.
2/3rd chance you picked incorrectly
1/3rd chance you picked correctly.
If you picked correctly, bob barker opens one of the losing doors. If you switch, you lose.
you picked one of the two incorrect doors. Bob barker swings open the other incorrect door. if you switch, you win. There are two ways to do this (one wrong door, or the other wrong door, either way the result is the same if you switch.)

Thus there are 2 of 3 ways to win with a switching strategy.

>> No.3357605

>>3357599

FTFY:
pick a door
open the door
get on the floor
walk the dinosaur

>> No.3357618

>>3357599
what if you pick the correct door the first time and the host open an incorrect one leaving the other incorrect one. in that situation it is not advantageous to switch

>> No.3357621

Show him the Monty Hall Problem with 10 doors. After he selects one, reveal 8 goats and ask if he wants to switch. He'll see.

>> No.3357622

>>3357618
the point is you don't know if you're on correct or incorrect door/.

>> No.3357632

>>3357618
and the probability of that situation arising is one out of three

>> No.3357642
File: 44 KB, 1024x768, monty.png [View same] [iqdb] [saucenao] [google]
3357642

If anyone's having trouble with this, check out my highly professional diagram

>> No.3357652

>>3357597
So he somehow thinks the problem involves repeated sampling?

>> No.3357663

>>3357597
Does he believe that the probability of a coin flip coming up heads is lower than 1/2 because the probability of getting 50 heads out of 100 flips is low?

>> No.3357664

>>3357621
actually yeah, do this, it's easy
just use 10 cups and a ping pong ball

watch your roomate struggle for an explanation after switching has won the "car" an overwhelming majority of the time

>> No.3357665

>>3357652
No, it's because margin of error increases as sample size decreases, and your sample size is one go at the game.

>> No.3357674

>>3357663
idk. going by his logic he might say that it isn't exactly 1/2, but you don't know whether it's higher or lower. again, confusing margin for error with the probability itself

>> No.3357681

OP, you should give him a go at the birthday paradox

>> No.3357686

>>3357652
retard is trying to do statistics in a probability question
fucking retard

>> No.3357702

>>3357665
>No
>sample size
sample size = statistics
gtfo

>> No.3357756

>>3357702
>>3357686
statistics and probability are intertwined. It's not unusual to look at one to conceptualize the other. Even the resulting argument is flawed it's on the right track and can be logically refuted.