How long does it take to recover from public humiliation ?

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Vos Savant's response was that the contestant should switch to the other door (vos Savant 1990a). Under the standard assumptions, contestants who switch have a
2/3
chance of winning the car, while contestants who stick to their initial choice have only a
1/3
chance.


After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong

Eventually though, many of those who’d written in to correct vos Savant’s math backpedaled and ceded that they were in error.
Tldr higher iq destroys Brainlet Mathematical community

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How math can show flaws in our common sense is pretty cool

You are a biologist traveling in the rainforest when you are bitten by a venomous snake. Luckily you know that the female of a certain species of frog native to this rainforest secretes the antidote to this venom on its back. You also know that only the males of this species croak. You see one such frog in front of you sitting silently. At the same time, you hear a male croak behind you and turn around to see two frogs of the species. You only have enough time to run to the lone frog you first saw or the pair of frogs behind you and lick their backs before the venom incapacitates you. Which do you run to and why?

what kind of faggot starts an argument about basic math with "well I have a phd and..."

Like, why did these insufferable morons even volunteer the information that they had phds

people like that are why normies don't respect academics

Too bad the goat is better

I've heard this problem multiple times. I would say the answer is it doesn't matter, because all of the frogs are independent of each other, so the single frog is 50% M or F, and the other group has one male and one other frog which is 50/50. However, I've seen some answers saying that it does matter. what's the explanation for your choice mattering?

Your conclusion is correct but your reasoning is wrong. You're missing something.

What is the proper reasoning? I can't think of any other factors.

what does it mean that we saw the one sitting silently?

might it be male, and we just so happened to not hear it croak yet? what is the probability of that?

I believe the one we see sitting silently means that we haven't heard a croak, so it could be male or female. also, assume for all frogs that it is 50/50 male or female unless it has croaked, which proves it is male.

The two frogs have a better probability than the one frog.
One frog has two possible states: 50% male, 50% female
Two frogs has three possible states: 50% male + female, 25% two females, 25% two males
Hearing a croak excludes the possibility of two females, which changes the probability distribution to 66% male + female, and 33% two males.

what if the goat is your goal

That doesn't make sense. the chances are 25 MM, 25 FF, and 50 MF. Even though you know that it isn't FF, when the frogs first appeared, these were the odds. even though now you know it isn't FF, it was still an option at first, so the odds don't change

Trivial inversion of the problem which upon inspection presents no new information. The real intent of the problem is to go for the more desirable thing in such-and-such a way.

Good questions, you're getting warm.

The states are not simply male and female. You have:

1. M croak, M no croak
2. M croak, F no croak

Are these states equally likely? Figure it out.

Of course the information that FF is impossible changes the odds. You can't have 25% chance of MM, 50% MF, and 0% FF. They have to total 100%. However, none of you have fully described all the information available, which leads you to the wrong answer.

giv highiq gf

here apu

contestants do not improve or lower their chance of winning the car by switching doors, unless you make the non-standard assumptions about the game host

anything saying otherwise is just logic foolery

I haven't taken a course on probabilities yet but the lone frog seems best. That frog has a 0.5 p of being the right one. On the other hand, given a random frog you have a .25 p since first of all you have to pick the one that didn't croak (0.5) and then if you got it right there is only a 0.5 chance of the other one being a female. Obviously going with the lone frog is better.

first you pick a door at random. There is 1/3 chance a car is behind that door. Then goat is revealed. Now you switch. 1/3 times you will lose, since car was behind the door you chose first. But 2/3 times, it wasn't. So you win.

>That frog has a 0.5 p of being the right one.
Sorry but that's impossible. I told you that females don't croak while we already know males at least sometimes croak, so how can you say a frog which you didn't hear croak is equally likely to be male or female? If I told you males never give birth and then I told you my friend has not given birth yet, that tells you my friend is more likely to be male, as no possible male friend would have given birth by now while at least some possible female friend would have. Get it?

>On the other hand, given a random frog you have a .25 p since first of all you have to pick the one that didn't croak (0.5) and then if you got it right there is only a 0.5 chance of the other one being a female
I said you can run to the pair and lick their backs you don't choose between them.

I bet Helene used this to justify always betraying everyone

Fuck off already, your incoherent rambling is pathetic.

is her iq 228? I wan 228iq gf

>Get it?
Sure I get it, but that information is useful only if you know the average rate of croaking. Say if a male frog croaks on average once every 20 seconds sure that will weight the probability toward being a female if it hasn't croaked, but it's meaningless without knowing that. What if they only croak a few times a day, completely at random?
It's the same with your friend, your statement is only valid if I know your friend's age, then I can calculate the probability that a female of age n has already given birth, which obviously increases as n increases. But without knowing that, I would need either your age and the distribution curve of the ages of the friends of an n years old person. This would make the calculation less accurate, because I would have a probability of your friend being of a certain age, and the probability of a woman that age having given birth.

>I said you can run to the pair and lick their backs you don't choose between them.
Right, so you can

logic foolery
1/3 chance you pick the correct door out of three doors
1/2 chance you pick the correct door out of two doors

there is nothing changing the odds you pick the right door the second time based upon what you picked the first time. they're unrelated.

hasn't anyone modeled this on matlab or python or something?

Why is his conclusion correct? The lone frog has a 50/50 chance of being male.

In the pair of frogs, we are faced with two options:

F/M pair: 50% chance of licking the male

M/M pair: 100% chance of licking the male

Both events are equally likely, so that gives us a 75% of being successful with the pair of frogs

fiftyexamples.readthedocs.io/en/latest/monty-hall.html

>Switching won 6639 times out of 10000 (66.39% of the time)
>Not switching won 3357 times out of 10000 (33.57% of the time)

NON SWITCHERS BTFO
ENJOY YOUR GOATS

>Sure I get it, but that information is useful only if you know the average rate of croaking.
Oh? Because the question did not ask for the specific probability. It simply asks which is better and why. You can compare them while keeping the chance of a male croaking while you were listening as a variable.

Well in the end without any extra data both choices are the same, because the extra frog might as well be an exact copy of the lonesome frog. Without any other knowledge all you can compare is the time they've gone without croaking and it's the same for both.
The only thing I could argue against going for the two frogs, is that you don't know if the non-croaking frog just got there from somewhere else where you couldn't have heard it croak, while you know for sure the one in front of you hasn't croaked.

yes
pls no buli

>Why is his conclusion correct? The lone frog has a 50/50 chance of being male.
No. See >In the pair of frogs, we are faced with two options:
>F/M pair: 50% chance of licking the male
>M/M pair: 100% chance of licking the male
>Both events are equally likely, so that gives us a 75% of being successful with the pair of frogs
Also incorrect. There are two states which are NOT equally likely:

1. M croak, M no croak
2. M croak, F no croak

Also, you want to lick the female, not the male.

Also, if the chance of male/female was 50/50 (i.e. we inappropriately ignore the croaking) MF would still be twice a lively as MM. You just made every mistake you could make.

You got it wrong. The rate of croacking may change the probabilities, but still one will be even marginally higher than the other.

>Well in the end without any extra data both choices are the same, because the extra frog might as well be an exact copy of the lonesome frog.
Yes that's the correct answer. You see, I purposefully worded this problem in order to fool both probability novices and people familiar with similar sounding problems (specifically the boy girl problem). The answer is intuitive, but not for an intuitive reason.

Explain.

From a biologist's point of view the answer is to check for sexual dimorphism, as frogs always have very noticeable differences between males and females. Males in particular tend to be very brightly colored, but as long as the frogs behind you are noticeably different from one another then go and lick those.

Both frogs go on for the same time wothout croaking. Since they both don't croak, it doesn't really matter. If one was to come later, that would be an entirely different problem.

This is a very rare species which has no visual dimorphism from the distance you are at. Croaking is also not associated with attracting females or threatening other males. As a biologist you know all this, which is why nothing to the contrary is stated in the problem.

Yes, that's what the guy you replied to said. What did you mean by "but still one will be even marginally higher than the other."?

Neat. If I survive I'll have a paper published in Nature after discovering a frog like that.

Misread the problem. I thought the croaking frog was the desirable one. At this point, if you were to introduce either frog earlier, the pair would still give you the best chance of survival.

>You see one such frog in front of you sitting silently. At the same time, you hear a male croak...

You didnt read the problem closely enough. The information provided states you observe them at the same time.
Thus your phrasing of "didnt hear croak" is an incorrect statement.

youtu.be/o_djTy3G0pg

No the pair gives you the exact same chance of survival. Specifically it's 1/(2-x) where x is the chance of a male frog croaking.

Also it seems silly to assume a frog was so far away that you couldn't hear it croaking and then suddenly hops up behind you.

>You didnt read the problem closely enough.
Considering I wrote the problem with exactly that wording in mind, I doubt it.

>The information provided states you observe them at the same time.
>Thus your phrasing of "didnt hear croak" is an incorrect statement.
That doesn't follow. I only started you heard a male croak behind you. Not multiple croak or multiple frogs croaking. Thus one frog behind you did not croak while you were listening.

sorry i just didn't wan brainlet gf

Suppose you're on a [family] game show, and the wife is given the choice of 10 doors: Behind one door is a car; behind the others, goats.

She picks a door, and the host, who knows what's behind the doors, says "you know, this isn't reasonable" and opens 8 other doors, which all have a goat.

He then says, "There, now there are just two doors to choose from. Behind one, a goat, and the other, a car."

The husband now comes in, not knowing what has happened before and only seeing two doors, and the host says to him,
"Behind one of these doors is a goat. The other, a car. You can choose which door to open, or you could decide to stick with your wife's decision, as she has already picked one of the two doors. Which do you choose?"

What does the husband choose? One of the two doors, or does he stick with his wife's choice from when there were 10 doors?

always switch

*when the host knows

She was being a twit.

The rules governing the host's behavior weren't described, but she assumed that he knew what was behind each door and would always choose a goat to reveal.

That makes her solution work, but it's an unreasonable assumption with the information presented. If the host simply opens a door at random, then switching doesn't improve your odds (although he may reveal a car, in which case you know you lost whether you switch or not). If the host decides whether to open the door and offer you a chance to switch based on what's behind the door you picked, then switching is either a sure win or a sure loss, depending on whether you choosing the goat or the car triggers his action.

So whether the choice matters, how much it matters, and whether switching is the right thing or the wrong thing, all depend on unstated assumptions about the host.

The worst thing is all the asshats who go around repeating her error, and being all Black Science Man about how wonderfully counterintuitive probability can be.

>You pick a door, say No. 1, and the host, who knows what's behind the doors
Reading comprehension of a babby desu

>That makes her solution work, but it's an unreasonable assumption with the information presented. If the host simply opens a door at random, then switching doesn't improve your odds (although he may reveal a car, in which case you know you lost whether you switch or not).
It's a very good assumption considering there is no reason a game show would want to risk showing the car thereby ruining the game and having to start over.

door 1 door 2 door 3 door 4 door 5 door 6 door 7 door 8 door 9 door 10
car goat goat goat goat goat goat goat goat goat
goat car goat goat goat goat goat goat goat goat
goat goat car goat goat goat goat goat goat goat
goat goat goat car goat goat goat goat goat goat
goat goat goat goat car goat goat goat goat goat
goat goat goat goat goat car goat goat goat goat
goat goat goat goat goat goat car goat goat goat
goat goat goat goat goat goat goat car goat goat
goat goat goat goat goat goat goat goat car goat
goat goat goat goat goat goat goat goat goat car

wife picks door 1
Doors 3-10 are eliminated as goats

door 1 door 2
car goat
goat car

Husband gets to choose door 1, or door 2, or his wife's choice(door 1).

You can see that it doesn't matter. Just like how it doesn't matter if you switch in the original Monty Hall problem. Everyone has just been logically bamboozled by the 2/3rds grouping nonsense.

>wife picks door 1
>Doors 3-10 are eliminated as goats
No, Monty picks the doors specifically to avoid the car in all cases, not simply in the cases where the car is in 1 or 2. Moron. This gives the contestant information that the car is most likely where she picked after Monty removes the other options.

Is this bait? If you pick door 1 there is a 1/10 chance that you picked a car. You showed it yourself with your little diagram.

>>That frog has a 0.5 p of being the right one.
>Sorry but that's impossible. I told you that females don't croak while we already know males at least sometimes croak, so how can you say a frog which you didn't hear croak is equally likely to be male or female?
Either you're a complete idiot, or you're harping on an irrelevancy... which makes you a complete idiot, so...

It's natural to assume that, since it hasn't been stated otherwise, a given frog absent sex information is equally likely to be male or female, especially given all the other unstated assumptions we're expected to make.

In any case, it doesn't matter, because the probability of a given frog being female, absent other information, doesn't affect the correct choice.

Anyway, the unambiguously correct answer is to go for the lone frog, even if you stupidly assume that catching a frog is always a sure thing and never involves any delays or complications, because if you go to the two frogs, you're guaranteed to lick a male frog, thus suffering the act of licking a frog for no benefit.

To elaborate:
case 1
don't switch
case 2
switch
case 3
switch
case 4
switch
case 5
switch
case 6
switch
case 7
switch
case 8
switch
case 9
switch
case 10
switch
If you pick door 2 it's the same except you should only not switch for case 2 and switch for case 1. And so on so forth

>Monty picks the doors specifically to avoid the car in all cases.

That's not even contested. Obviously, that's how the Monty Hall problem works.

It doesn't matter what door the wife picks. The Host gets rid of all but 1 goat. The wife either selected which goat stays, or she picked the car and the Host selects which goat stays.

Either way in the end one door has a goat, and one door has a car.

this is obvious bate but i'll bite.

expand the monty hall problem to 1000 doors. a single door has a car. 999 doors have a picture of BBC.

You pick door x. The host removes every door except door x and door y. The prize is guaranteed to be behind one of these doors.

Do you stick with your original door which you picked with a .1% chance of finding a car? Or do you switch doors where you now have a 50% chance of winning a car?

Lets take that back to the original question.

Your first choice had a 1/3 chance of winning.

after the host removes one door if you do not switch doors you still remain at a 1/3 chance to win. If you choose to switch doors you now have a 1/2 chance of winning.

>1/2 chance of winning
btw this assumes these as independent events.

If you look at this as a related event, you actually have a 2/3 chance of winning because out of the original 3 doors you get to pick a second

>Either you're a complete idiot, or you're harping on an irrelevancy... which makes you a complete idiot, so...
So instead of trying to understand what I'm saying and how it relates to the problem you are just going to react to it and eventually realize your mistake. Let's see how long that takes.

>In any case, it doesn't matter, because the probability of a given frog being female, absent other information, doesn't affect the correct choice.
It does if you are going to properly explain the correct answer, instead of just intuiting it.

>It's natural to assume that, since it hasn't been stated otherwise, a given frog absent sex information is equally likely to be male or female, especially given all the other unstated assumptions we're expected to make.
Yes, and you have been given sex information. A lack of croaking gives a higher probability of being female, since females never croak.

So far nothing you've said actually counters what you're replying to. Your post is useless.

Shit like this is EXACTLY why mathematicians have settled on a standard definition of probability with a rigorous, formal specification of its associated properties:
To prevent semantic ambiguity in loosely-worded scenarios, that give rise to implementation-defined calculations.

>That's not even contested.
You did contest it by only presenting possibilities in which Monty reveals doors 3-10 in your illustration. By ignoring the other possibilities, you removed 8 of them in which switching would get you the car.

Basic probability question assuming even male/female ratios:

frog in front of you:
.5 chance of female.

Frogs behind you:
one is male (0 chance female)
one is maybe male (.5 chance female)
total: .25 chance female

easily verifiable with a simple diagram

Mark my words and mark them well.

I will destroy the Monty Hall Problem and you will live to see it.

not user you were arguing, but is this diagram correct? Or is it missing something?

This reasoning is the most retarded thing since Monty Hall. I'm not saying you are conveying your thoughts wrong. I'm saying your thoughts are shit.

I think your thoughts are shit because you have none except ad homs and big black penis

your chance of getting the big black penis increases if you switch from ad homs

stop thinking about black penis

it's 50% either way since you heard a croak behind you, meaning one of the frogs is a male for sure (if you are assuming the croak came from one of the two frogs), and there's a 50% chance of the 2nd being a female, same as the 50% chance of the silent frog in front of you.
unless im missing something

monty hall problem you switch, always, it's easily testable

I have a 50% chance.

at least you admit it

monty hall is wrong because it assumes the information is transferred when the door is opened, yet the information assumes a car to be a goat. it would work if no doors were opened, then you could switch and get your result.

this stupid frog antidote doesn't work because the probabilities in the two frogs case add, not multiply.

But did the croak really come from one of the frogs behind you?

you keep writing it, so you have a 100% chance :^)

How can a person be so wrong? Did you try being as wrong as humanly possible?

i mean, i think you have to assume it did. If you don't (which i wouldnt, since you just saw 3, there could easily be a 4th!), then for sure you would want to lick 2 instead of one.

he's right about the Monty Hall problem

he's wrong about the frog problem, but that's because it's a poorly constructed problem

Nah, I'm not a mortal like you :)

>then for sure you would want to lick 2 instead of one.
Actually, I think thats the obvious solution.

why not turn around and grab both frogs?

Where is he right about the Monty hall problem? Modeling the situation in a computer simulation agrees that switching is always better.

Nope. See

desu I haven't thought as much as the frog problem as I did with the Monty, but the way I see it (I may have misunderstood the problem btw):

You turn around, you have two frogs, one of them is CERTAINLY a male. Thus, remove it altogether from the equation.
So, the probability of licking the female frog in two iterations is 50%. One of the two frogs is bound to be a miss.

models are built to confirm what the logical bumblefuck of bad math predicted

Look at the thought experiment I have written. How is it possible if the no doors opened gives the exact 2/3 solution when you switch? Then what does the door opening even mean?

Work your way from there.

ok I get it, it's multiplicative. I actually feel like I can work my way to the Monty setting from the frog setup. That would be nice

In order for it to be 50%, males would have to be as likely to not croak as females. But we already know that's not true. Try again.

What I mean by no doors opened, is that you don't reveal what is behind the door yet you remove it nevertheless.

Obviously for the lone frog it's 50/50

For the pair of frogs, the three possibilities are (presented with the gender of the croaking frog first)

M, M
M, F

Thus if you lick the two frogs there's a 50% you lick a female.

>three possibilities
>lists two possibilities
The fuck

it's not actually easier to get the goat than to get the car lol
maff amirite

>Obviously for the lone frog it's 50/50
Wrong. That would imply a male frog is as likely to not croak as a female, which we know is false.

>M, M
>M, F
>Thus if you lick the two frogs there's a 50% you lick a female.
Wrong, those possibilities are not equally likely, for the same reason as the above.

The problem definition is shit. The user is right.

>that moment when dumb frog poster blows everyone the fuck out

but nothing in the puzzle said anything about males always croaking, or a time limit for croaking. The silent frog could be a male or female with the information given. The croaking you heard is one of the frogs behind you, assuming the croak came from one of the two frogs and not a 4th frog.

Typing is hard