Thread 106227140

This is one the most counter-intuitive and at the same time simple paradoxes. I still don't get it, but it just werks.

>>106227140 (OP)
it's over for mathlets
time to get a real engineering degree
software "engineering" is just a meme

>>106227140 (OP)
G G C
pick one

G -> G | C
G -> G | C
C -> G | G
if you pick a goat door he will remove the other goat door. if you picked the car he will also remove a goat door
G -> C
G -> C
C -> G
so as you can see in 2/3 cases its better to switch door

what is counter intuitive about it OP ?

>>106227285
>Many readers of Savant's column refused to believe switching is beneficial and rejected her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them calling Savant wrong.[4] Even when given explanations, simulations, and formal mathematical proofs, many people still did not accept that switching is the best strategy.[5] Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating Savant's predicted result.[6]
>The problem is a paradox of the veridical type, because the solution is so counterintuitive it can seem absurd but is nevertheless demonstrably true.

People are just retarded and don't understand that the host will never open the prize door. That's what makes switching better.

>>106227285
>what is counter intuitive about it OP ?
It's easier to understand when visualized like this, but ordinarily it is difficult to see the information gained by the goat door being removed. It seems like a simple 50/50 choice
>>106227253
Mathematicians of a way higher caliber than you were fooled, and you would've been too, were this not one of the most well known paradoxes.

>>106227140 (OP)
Take it to the extreme. imagine that instead of 3 doors, there was 1 million doors. Then the guy opens all but your door and one other and asks if you want to switch.

>>106227396
Wow so mathematicians are actual retards like everyone else who reject reality when it hurts their feefees (makes them feel stupid).

>>106227140 (OP)
> you have low information and make a decision
>oracle gives you more information
>your next decision is better informed
Never understood what was "counterintutive" about this. Maybe some less evolved breed of humans assume that their choices are always correct?

When you can decide you have a locked door a closed door and an open door, the locked door has a 1/3 chance of winning back from when you chose it, the open door now has a 0/3 chance, and so the closed door now has 2/3 chance of winning

>>106227469
Statistics is not science. It is also always 50/50, either you do it or you do not.

>>106227562
No one claims that sticking with the door will result in a 100% probability of a win, retard.

The basic decision is chosing between 1 door and 2 doors, and if you chose 2 doors you have more chances of picking the right one.

You get given information after the first choice but that information is irrelevant, what matters is the host lets you change your decision in a way that lets you pick a larger amount of doors.

It's pretty intuitive if you increase it to 100 doors.
You choose 1 door out of 100. The chance of getting it right is 1/100 or 1%.

The host offers to close 98 wrong doors and leave one door left. This set of 99 doors has 99/100 or 99% chance of being right.

Monty opens the 98 of 99 doors but they still belong to the set of 99% probability, so the one door lefts inherits that probability as 98 goats have been removed.

Now just reduce it to 3 doors.

You pick one, probability is 1/3 or 33.333% of it being correct.

Monty now offers the other set of doors containing 2/3 or 66.666% of being correct.

He opens one of the doors, but he ALWAYS opens the goat one. If he did it randomly it would be 50/50. But because he chooses a set where he always opens the goat ones it keeps the set probability of 2/3'rds.

>>106227718
I think that's the main reason why the whole thing is counterintuitive. Concepts like "right" and "wrong" do not exist in probability theory, instead one has to reason in terms of the result of a large number of experiments.

You get invited to the TV show every month, each time asked to chose between 1 and 2 doors.

>>106227777
Okay now I get it
It's basically what's the chance of you choosing the correct door vs the chance of the host choosing the correct door for you.

OK /g/ try this one
you choose 1 in a million doors all duds but 1 car. The host opens 1 other door to reveal a dud. Do you switch?

>>106227843
The trick is that the host ALWAYS opens wrong doors while offering you the switch.

Because he always opens wrong doors and we already know this nothing changes when he opens them.

The probabilities of the two sets remain the same 1/3 vs 2/3.

If the host opened random doors and risked the car showing before the switch, and a wrong door was opened, then the probaility would in fact be 1/2 (50/50) when he offered you the switch.

But because they cant risk the right door being opened before the offer, they always open wrong doors, and thus the probability sets are conserved.

>>106227285
>>106227396
>>106227446
>>106227777
The question never said that the host will always reveal a goat

>>106228062
>the host ALWAYS opens wrong doors while offering you the switch.
No, you still have 33% chance of picking the wrong door when chosing the 2nd option.
The host just changes the game rules from picking 1 door to picking 2 doors. Knowing it's not door #3 is just pointless drama for the audience, the information is completely useless.

>>106228171
Yes, you highlighted the part of the code that wasn't stated in the Monty Hall problem. Good job.

>>106228225
SARRRRRRRRRRRRRRRRRRR

>>106227140 (OP)
>"Switch doors? No thank you. I'm pretty sure I chose the correct door."

>>106228262
Lol. Did you really take a screenshot, underline text, fill out a captcha, type out a message, and still not realize your mistake?

Where in the question does it say that Monty picks a goat 100% of the time? For all we know he is picking between two goats and has no choice. For all we know he is picking randomly. For all we know he is trying to pick a car but cannot because the contestant has picked the car. Go ahead and highlight the part that tells us how Monty picks his door, I will venmo you a billion dollars if you can find it

Math are wrongs every knowedge come from practice

>>106228321
Holy esl

>>106228321
Keep your one billion rupees, Rajeeb.

https://www.tandfonline.com/doi/abs/10.1080/00031305.1975.10479121

>>106228403
>>106228406
Yes yes Monty Hall would CERTAINLY pick the door with the goat, right fellow mathematicians? That's totally how probability riddles work, no need to state it in the problem, just assume it's rigged because of cultural context clues about TV shows often being rigged. Go ahead and include that in your proof for the problem, that's a totally heckin valid answer :)

>>106228510
It's written clear as day in the problem text, Rajeeb. Now go back to sniffing curry or whatever it is you do these days.

>>106228529
You are welcome to point out where it's written. You've taken two screenshots with underlined text already, go ahead and show the class where it says Monty will always pick a goat. Within the problem, this time.

>>106227140 (OP)
Think about it like this image u have 10000 doors, and u pick one, now the commentary asks u if u want this specific door and asks u to choose, what's more likely u having picked the 1/10000 or this other door and remember u can only win or lose

>>106228558
Rajeeb, I've already underlined it in the original American Statistician article from 1975 where the problem was introduced for the first time: >>106228406.

Monty does not open the winning box. It says so here and everywhere else clear as day.

I don't know why you're being a fucking retard but maybe it's just an indian thing. Anyway I'm out, good luck to you and your curry nation.

>>106228642
>Within the problem, this time.
It's amazing how incompetent you are

What I like the most about these problems is how many different reasonings people come up with.

To me, it boils down to:
>there's more goats, so you had more chance of picking a goat at random
if your original choice is more likely to be a shit choice, then, of course, you should swap it

It's the same exact thing with the silver and gold balls in boxes, but even more confusing, because people assume that picking an all-silver box *never* happens because the question talks about a single instance where it didn't happen.

>>106228292
"I'm not into cars. I could use a goat though."