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# [Poll] Can YOU solve the frog riddle?

Registered User regular
So this video is driving me up a wall lately.

It’s a riddle about probability, which already is gonna cause some arguments.

Basically, you’re poisoned, and you need to find a female specimen of a certain type of frog to cure yourself. The frogs have a 50:50 ratio of male to female. The frogs have no visible differences between the sexes, so the only way to tell them apart at a glance is that the male has a distinctive croak.

You see one frog on a stump, but then you hear a male frog’s croak from a clearing that contains 2 frogs, and you don’t know which one croaked. Which frog(s) should you move towards for the best chance of survival?

Effectively, this is a riddle about coin tosses. Each side (sex) can come up 50% of the time for any given coin (frog). You need to find at least one tails (female) result to succeed. On one side, you have a single coin (frog) whose result is completely unknown. On the other hand, you have 2 coins (frogs), one of which is revealed to be heads, but you don’t know which position it was in when they were tossed.

————

The video itself claims that the set of 2 frogs has a 3/4 chance of having the needed result. They say it’s because in any group of 2 coins, there are more combinations with least one tails result than there are with no tails results (HH, HT, TH, TT). But that seems completely wrong to me. If one coin is heads, then the chance of one remaining coin being tails should be whatever the chance of a single coin landing tails is: 50%. The argument for this is that a specific coin (frog) is heads (male). Even if you don’t know which position it was in, the results do. So instead of (HT, TH, HH), we’d be looking at (HT, HH), because the coin that landed heads is specific, even if it’s a mystery.

This damn video has been living in my head, because it seems totally wrong, and its comments are a firestorm of arguments about the probability of these damn frogs. What do you think? Which set of frogs is more likely?

## [Poll] Can YOU solve the frog riddle? 49 votes

The pair of frogs is 75% likely to save your ass
22%
They’re both 50%. Flip a coin, lol
28%
Larlar
48%

## Posts

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boom Registered User regular
why can't i pick the first frog up and take it with me

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Registered User regular
They’re both 50%. Flip a coin, lol
why can't i pick the first frog up and take it with me

There’s no time. By the time we finish writing up a chart of probabilities, we have 2 seconds to live.

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boom Registered User regular
i tried to eat this frog and it was just a goat!

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Registered User regular
Larlar
The video says the chance of surviving is 67% and not 75% at the clearing, and the video is right.

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Tiny Bat Registered User regular
Bring the first frog to the other two and see which ones try to bone which ones.

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Registered User regular
They’re both 50%. Flip a coin, lol
discrider wrote: »
The video says the chance of surviving is 67% and not 75% at the clearing, and the video is right.

Oh dang it.

I’ve spent so long arguing in the comments that I haven’t watched the video in full for a bit.

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boom Registered User regular
the primary reason to become a statistician is to construct scenarios that when you reveal the math to people makes them go "hey fuck you"

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GNU Terry Pratchett Registered User regular
Larlar
Aistan wrote: »
Bring the first frog to the other two and see which ones try to bone which ones.

Wow, this gay frog erasure

[Muffled sounds of gorilla violence]
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Registered User regular
edited February 2022
Larlar
We need to be study the species of frogs to determine the probability of the two frogs in the clearing boning and how that relates to gender, if at all.

discrider on
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Registered User regular
Larlar
At least this problem isn't Monty Hall

(There are three frogs.
You're pretty sure only one of them is female for some reason, but can't tell which one.
As you move towards a frog, one of the other two croaks.
Do you continue to move towards your chosen frog, or towards the other frog that didn't croak?
Yes you always change frog
)

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Registered User regular
Short answer: Both are wrong, it's somewhere between the two depending on the probability of hearing a croak from a single male frog in the given time period.

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Registered User regular
edited February 2022
Larlar
Nah that analysis changes the problem.

This problem intends to ask a similar question to:
'do you choose the stump or these two frogs in an illuminated circle with a flashing arrow pointing at it saying "at least one of these frogs is male"'

And I'm not sure how the probability of observing a male frog in a constructed circle makes sense.

..
It's probably 1.
The chance that the frog croaks is one because the problem makes him croak.
The chance that the frogs sits on this flashing display case is one because the problem made him.

Which collapses the analysis to the TED answer.

discrider on
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Registered User regular
edited February 2022
I got it wrong but the answer makes sense

Frog on the stump has 2 equally probable options
Frogs in the clearing have 3 equally probable options, 2 of which mean one of the frogs is female

As always I recommend turning this into a real life betting game to fleece your stubborn friends out of money

Quantum Tiger on
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Registered User regular
The two frogs in the clearing is worth one on the log.

(I go where I know there is a malefrog, the statistical analysis is irrelevant)

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Frictionless Spinning The VoidRegistered User regular

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Registered User regular
Larlar
What's the probability that male frogs like getting licked

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GNU Terry Pratchett Registered User regular
Larlar
The two frogs in the clearing is worth one on the log.

(I go where I know there is a malefrog, the statistical analysis is irrelevant)

But it's the ladyfrog you want

Assuming that your goal is finding the antidote as opposed to something unrelated to the issue at hand

[Muffled sounds of gorilla violence]
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In the scuppers with the staggers and jagsRegistered User regular
Go to the clearing. If they both turn out to be male, at least your last experience on earth will be listening to frog fight noises, which are cute and hilarious.

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This is also my fault Registered User regular
Male frogs croak in order to attract a mate. You heard a male frog in the clearing with two frogs, therefore it's more likely that the clearing contains both the known male frog, and a female frog he's attempting to attract.

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Registered User regular
edited February 2022
They’re both 50%. Flip a coin, lol

One frog place, your possible outcomes are:
Male
Female

2 frog place, your possible outcomes are:
Male/male
Male/female

What the fuck

Captain Inertia on
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Registered User regular

but yeah if you assume a perfectly spherical frictionless frog in a vacuum the two frogs is the better chance.

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Registered User regular
They’re both 50%. Flip a coin, lol
Can’t frogs change genders or is that another thing Jurassic Park lied about

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Registered User regular
edited February 2022
They’re both 50%. Flip a coin, lol
The video’s logic contradicts itself. And it seems to be all based on how many frogs I can lick.

If I go to the clearing and I can lick BOTH frogs, then my chances of living are still 50/50. Because we know one of those frogs is male, then we’re still really only flipping one coin on the other frog.

It doesn’t matter if the male is on the left or the right (as their chart points out) because I’ll be licking them both. We know one of the frogs is useless, but we don’t know which one, but it’s friend still only has a 50/50 chance.

Perrsun on
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Call me SkraggRegistered User regular
Larlar
Eat all 3 frogs. Just munch them up.

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Registered User regular
the primary reason to become a statistician is to construct scenarios that when you reveal the math to people makes them go "hey fuck you"

This was me for the entirety of my statistics class in college.

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Registered User regular
Obviously the answer is to leave the frogs alone and let the poison fester in your body so you can build up "natural immunity". After all, who knows what's in the female frog, could be anything. But we know the poison is poison so we'll probably survive, Joe Rogan told me so.

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Registered User regular
Lay down and die easy next question

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This is also my fault Registered User regular
Perrsun wrote: »
The video’s logic contradicts itself. And it seems to be all based on how many frogs I can lick.

If I go to the clearing and I can lick BOTH frogs, then my chances of living are still 50/50. Because we know one of those frogs is male, then we’re still really only flipping one coin on the other frog.

It doesn’t matter if the male is on the left or the right (as their chart points out) because I’ll be licking them both. We know one of the frogs is useless, but we don’t know which one, but it’s friend still only has a 50/50 chance.

This has to be correct. The greater than 50% chance of a female frog is only present in a scenario where you can only lick one frog. The math as presented is treating the potential for a FM or MF as differing scenarios. But we can lick both, so it doesn't matter.

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No face Registered User regular
They’re both 50%. Flip a coin, lol
I go for the frog I already have in my sight rather than risk scaring off the two I can only hear from blundering through the brush. Do you even know how fast those suckers can move?

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No face Registered User regular
They’re both 50%. Flip a coin, lol
Also if I die then it's not because of odds it's because several things have already gone horribly wrong in life to place me in a situation where I've been poisoned and my only cure is chasing amphibians.

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Registered User regular
Juggernut wrote: »
Lay down and die easy next question

Okay but what if licking a male frog kills you instantly I don't know that I want to wait for death's embrace.

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I will build a labyrinth to house the cheese Registered User regular
Male frogs are territorial so obviously if two frogs are next to each other and at least one is male and they aren't fighting, the other is female. Basic biology I don't know why we need all this math nonsense cluttering up the place.

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Registered User regular
Up Job wrote: »
Juggernut wrote: »
Lay down and die easy next question

Okay but what if licking a male frog kills you instantly I don't know that I want to wait for death's embrace.

I refuse to be a pawn to probability I will not only die I will kill the frogs before I go just to spite God and mathematicians.

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I will build a labyrinth to house the cheese Registered User regular
edited February 2022
Anyway, the video trips itself by having the parameters be that you know one frog in the clearing is male but you also don't have to pick one of the two. At that point. it doesn't matter that you don't know which is male, because you're just licking both frogs. We can discard the one known male as ancillary to the question. You have one unknown frog in each clearing. It's a coin flip.

If you had to choose one of the frogs in the two frog clearing, then the outcome spread of knowing one is male would matter and we'd get into the statistics fuck zone (although in that case the answer is go towards the lone frog because in the clearing you have a sub 50% chance of choosing a female if choosing blindly). But you don't have to choose and they asked a much less interesting question as a result.

3cl1ps3 on
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Registered User, Moderator mod
edited February 2022
They’re both 50%. Flip a coin, lol
I think an important rule that you left out of the question to make the 2 frogs answer make sense is that no matter which way you go you can only pick one frog to lick or whatever. The way the question was asked here implies you can either lick the one frog on the stump or both frogs in the clearing, which makes it 50:50 I think.

BahamutZERO on
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No face Registered User regular
They’re both 50%. Flip a coin, lol
What if licking a male frog is instant death, then you can't lick both.

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No face Registered User regular
They’re both 50%. Flip a coin, lol
I'm starting to think we haven't actually been poisoned we're just hallucinating that we've been poisoned and the only cure is to lick a frog.

Also we already licked a frog and that's why we're hallucinating in the first place, leading to a chain reaction of delusions as we leave a trail of extremely unhappy frogs in our wake.

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Here we may reign secure, and in my choice, To reign is worth ambition though in HellRegistered User regular
I think the way that the probability works out in the video makes a sort of sense (in the way that any probability ever makes any sense)

But as with many of these hypotheticals, I feel like trying to write a story around it overcomplicates it and makes it more confusing, rather than providing a grounding that you can use to try and figure it out for yourself

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I will build a labyrinth to house the cheese Registered User regular
I think it's really important to stress here that:

HH, HT, TH, TT

is a distribution of potential tosses based on the assumption that you haven't observed either of the tosses yet. Once you observe the first coin, some of the combinations become immediately impossible. It's also place agnostic, but if we have to specifically choose the female we can't be place agnostic because we need to choose a specific coin. We already know one of the coins is Heads, so one of HT or TH can't happen. To illustrate it visually:

HH HT TH TT

Let's take red H as our known male. He's already flipped a heads and we've confirmed that via hearing the croak. The outcome

TH

Is therefore impossible because we know the coin/frog that would be T here is definitely H. Blinding the frogs doesn't affect this - one of the coins is already flipped, you've observed the result, it is an H. The other coin has a completely independent probability.

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No face Registered User regular
They’re both 50%. Flip a coin, lol
Straightzi wrote: »
I think the way that the probability works out in the video makes a sort of sense (in the way that any probability ever makes any sense)

But as with many of these hypotheticals, I feel like trying to write a story around it overcomplicates it and makes it more confusing, rather than providing a grounding that you can use to try and figure it out for yourself

But if there's no story how can I take the piss out of the scenario? Math is just logic and sometimes puns, there's no material for me to work with.