/biz/ - Business & Finance

>>18617015

This is a well known conditional probability problem. Switching is the right answer (2/3 chance)

>>18617015
this question is such a meme by now, even people who dont understand probability know the correct answer

It's 50/50 because it states you already have a green ball so we start calculating from that point.

>>18617015
It does not matter

>>18617063
>>18617070

Please guys, OP even used the picture from the wikipedia article https://en.wikipedia.org/wiki/Monty_Hall_problem

>>18617086
I don't agree

>>18617042
>This is a well known conditional probability problem. Switching is the right answer (2/3 chance)

This
and it’s obvious OP now fuck off back to rebbit fag

You Punch out the host, kick in both doors, and wheel out in the Lambo getting dome from the stage model.

Chad gang

>>18617015
>-you understand probability, right anon?
No I don't

>>18617063
That was 2/3rds you nigger it was explained repeatedly

I don't switch so I have a better probability of getting my own goat

Lessons in critical thinking 101. Reminds me of the opening lines of one of my first lecture as a freshman by the shiftiest most incompetent but somewhat hot lecturer.

Then again I think I will take the goat. its built like a horse but can buck harder.

>>18617015
I didn't get this problem until right now, because I saw the other one with the green/red balls. For years I read this problem as there's only ONE goat, two doors safe. Durrrrr

Work out roughly the odds/probability of this accidently happening and I will maybe send you some Zenon if you are close to being right.

>>18617215
Actually, wait. There IS one goat left once a door is opened.

DOOR 1: GOAT
DOOR 2: NO GOAT (PICK)
DOOR 3: GOAT

Door 3 revealed.

DOOR 1: GOAT
DOOR 2: NO GOAT (PICK)

Why should I switch? If he is going to reveal a door anyway, the odds were 50/50 from the start.

>>18617243
Intuitively seems like it should be 50/50, but if you switch you have a 2/3rds chance of winning the car.

83% of PhDs got this wrong when it was published

>>18617015
The Monty hall problem
You should always switch
the host is giving you the right answer two thirds of the time because you are wrong one third of the times
https://www.youtube.com/watch?v=TVq2ivVpZgQ

>>18617257
>but if you switch you have a 2/3rds chance of winning the car.
But why? He would open a door with a goat, regardless of what you pick.

Yes in the future this may be argued similarly to
>>18617257
As the car is in a quantum super position until it is revealed.

>>18617284
When you picked a door, you had a 1/3rd chance of being right (1 of 3 doors has a car).

That means those 2 remaining doors, combined, have a 2/3rds chance at containing the car. So imagine drawing a circle around the 2 doors you didn’t pick. That circle has a 2/3rds chance of having the car.

Once the goat door has been opened, there is now only one door in that circle. You can switch to be in the circle.

>>18617261
oops i meant u are right 1 third of the time

*correction - simmilar to >>18617243

But under current theorem:
>>18617257
is correct.

>>18617163
this.

Literally none of this applies to trading. As a matter of fact, that question doesn't even apply to card counting like in that shitty movie.

>>18617328
>Literally none of this applies to trading.

Not directly. But training your mind to overcome the faults of instinctive human reasoning is useful for many complex pursuits.

>>18617284
>He would open a door with a goat, regardless of what you pick.
That's the answer to your question. There's three scenarios:
1. You pick goat A, the host opens the door to goat B. You switch and win the car.
2.You pick goat B, the host opens the door to goat A. You switch and win the car.
3. You pick the car, the host opens any door. You switch and lose.

>>18617309
Thanks for taking the time to explaining the theory, but I don't see it. Why does it matter what the chances were initially? A chance won't drive you around. Whether you win or lose is determined at the end, when you have a choice between picking a goat or a car, which is 50/50.

>>18617309
But that's just not true. Yes, prior to opening the goat door we would obviously want to open two doors instead of one, because yes that would be 2/3 chance. However, we've already eliminated one of the possibilities, one of the doors in this "circle" has been proven to be the non-car one. How are we left with anything, then, but a choice between one unopened door and another unopened door with equal chance of being the car?

>>18617372

No. I hope you're trolling, but here goes:

Imagine if there were 100 doors. You pick a door, and the host opens up all the doors except for one other door, revealing 98 goats.

There are now only two doors left, including the one you picked. Do you switch?

>>18617396
Think it through again. The door you picked has a 1/3rd chance of winning. So the circle you draw around the other 2 doors has a 2/3rd chance of winning. If you’re within that circle, you have a 2/3rd chance of winning. The car doesn’t move so that can’t change.

This runs through the options: >>18617356

You can make a quick chart and see the results yourself. It’s definitely not immediately intuitive at all for most people, myself included.

>>18617436
>There are now only two doors left, including the one you picked. Do you switch?
I'm not trolling. Why should I switch if we know from the start we're eliminating 98 bogus doors? The only one that will remain at the final decision is the one that I picked and a potential bogus one. I cannot lose with my initial pick, because the part where he's going to take out 98 doors has yet to come. Then I get to make a decision between two doors.

>>18617356
I can understand these problems only by doing this, is there another method one can learn or the only other option is to memorize the general rules?

>>18617480
When you picked, you had a 99% chance of being wrong.

When you know you have a 99% chance of being wrong, switching when 98% of the other options have been eliminated is definitely the right choice.

>>18617480

I encourage you to draw out the possibilities and look at them like >>18617356 has done.

The main point here is that the gameshow guy would never open a door with a car behind it. The gameshow guy is biased into opening doors that do not contain cars.
Let me try to explain my example again:

Since there were 100 doors, there is only a 1% chance that you choose the car on your first pick. The host opens 98 doors, but doesn't open the door with a car behind it. Do you think your initial pick was correct (1% chance), or do you think the door that wasn't opened contains a car?

>>18617436
>>18617519
>>18617480
Actually, fren, I get it now. Thanks. It only makes sense in my head when I visualize a million doors.

>>18617442
Thanks for trying to help me through this, I genuinely appreciate it. However, I still can't reconcile this: Yes, one door out of three is 1/3, two doors out of three is 2/3. I understand this. However, I disagree that just because the car's door hasn't "moved" means it remains 2/3 once one door had opened revealing the goat. Again, one of those 1/3 has been eliminated, completely, we know it is NOT the car. Why do we carry over the probability from this now-defunct...

I THINK I MIGHT GET IT?? It pisses me off, because I hate how these questions are fucking worded- I genuinely believe the questions themselves are dogshit, but I think I might grasp the mathematics.

I, however, think that said mathematics are also stupid because:

Yes, there are two instances out of three in which you could have picked one of the goat doors, and only one where you picked the car one. I find it baffling that this translates into a 2/3 possibility upon opening the goat door, however. Regardless of what choices you make, though. One of the goat doors is going to be eliminated by the gameshow host, this is a fact. I don't see any reason that there is a distinction between Goat A and Goat B. In either case, you have chosen a goat door and another goat door is eliminated. I don't think it's fair to treat them as separate instances, and then pair these two up with picking the correct door the first time and deriving our chances from there. Am I misunderstanding something?

>>18617015
The correct answer is

OP = FAGGOT

>>18617674
Essentially, think of it like this. Your chances of getting it right initially are less than 50% or 33.3%. But since there is a second round either way, your chances of getting it right the first time is still 33.3%. That's because the doors aren't eliminated pure randomly. But rather, think of it in game terms.

>PLAYER PICKS (DOOR)
>CHOOSE RANDOM (DOOR) OBJECT
>IF (DOOR) CHOSEN BY PLAYER IS [WINNER], ELIMINATE FROM RANDOMIZATION POOL, PICK ANY (DOOR) AND DELETE
Chances of you picking the door that has the [winner] variable is 33%.

>>18617674
The door the host opens doesn't stop existing and it definitely affects the outcome because it depends on the door you chose at first.

100 hours in MS Excel

>>18617528
Yeah, I think I might also understand now, maybe, after using some really big numbers? Thinking about it still pisses me off, mainly because I still believe the way these sorts of questions are worded are intentionally meant to trick your logic, but correct me if my reasoning is off:

If I have ten quintillion doors to choose from, I choose one. Bam, all the others but one open. How I'm able to wrack my brain around my odds is to think of it like this: I have either just made an astronomically lucky guess, OR the right door was in the other set AND the gameshow host just eliminated every single other one option except the right one.

>>18617844
Basically. You know when you chose your first door that there was a 99% the car was somewhere else. Now there’s only one door left “somewhere else”, and you can take it.

>>18617015
Just think of it like this:
Your initial probability is 1/3. 2/3 that the right door is not your choice.
Now the host offers you to keep your door, or switch to the other two doors.
Of course the probability is then going to be 2/3.

>>18617844
I think it's the fact that we can imagine the three doors as three apples or objects we can handle in reality. But once it becomes too difficult to visualize in real terms and you have to apply math (go abstract?), the odds become more obvious.

>>18617844
I think your main problem is that when you hear probability you only think of independent events. You should read about conditional probability.

>>18617015
stay. there was a 2/3 chance of goat. since the host can neither open your door, nor reveal the car. he will open the remaining door with the goat. with a goat at another door revealed you now have a 1/3 chance of goat, therefore a 2/3 chance of car if you stay. never doubt your decision

>>18617015
>post mildly interesting math problem that everyone knows
>100s of replies from trolls and retards taking the bait
every time

>>18617015
Another easy way to think of it is like this.
Suppose you never take the deal. Under no circumstances do you switch. Then the offer of switching may as well not happen. It doesn't do anything for your probability of being right. Therefore your probability of being right remains the same, which is 1/3.

But that means the probability of the other option being right is 1 - 1/3 = 2/3, since the sum of all probabilities must add to one.

This is also easy to simulate btw, for those who are more convinced by numerical experiments. This is a simulation of 1000 monty halls for example. The simulation returns 1 for a win and 0 for a loss. I then take the mean over n experiments and plot it. You can see the mean converges nicely to 2/3

>>18617674
Here's what made it click for me.

You initially have a 1/3 chance of guessing correctly. This means that it is likely that you are wrong with your first guess. So you simply assume that your guess is wrong and that you picked a door with a goat behind it. This is statistically likely, so we can start with that assumption.

Then the host opens a door with a goat behind it. Now if you assume that the door that you picked first also has a goat behind it, then the remaining door must have the money.

You have to assume that your first guess was wrong. That would be a correct assumption 2 out of 3 times, ie. the assumption is correct more often than it is not.

Does that make more sense?

>>18617124

If there were ONE THOUSAND (1000) total doors and you choose one and then your game show host opens the other NINE HUNDRED AND NINETY EIGHT (998) doors to reveal goats,

are you still going to fucking choose your original pick? AH?

Thought so.