An update on recent technical problems and more from the admin: https://forums.penny-arcade.com/discussion/250292/on-technical-difficulties-mod-coverage-and-other-things/p1?new=1

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Enlong
Registered User regular

So this video is driving me up a wall lately.

https://youtu.be/cpwSGsb-rTs

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?

https://youtu.be/cpwSGsb-rTs

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

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?

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

Oh dang it.

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

Wow, this gay frog erasure

discrideron(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?

Long answer

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.

discrideronFrog 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 Tigeron(I go where I

knowthere 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

https://www.youtube.com/watch?v=5Vb2pO7KQ_g

One frog place, your possible outcomes are:

Male

Female

2 frog place, your possible outcomes are:

Male/male

Male/female

What the fuck

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

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.

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

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.

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.

If you had to

chooseone 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.3cl1ps3onBahamutZEROonAlso 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.

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

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 TTLet'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

THIs 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.

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.