The frog riddle
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The frog riddle
https://www.youtube.com/watch?v=cpwSGsbrTs
Whats your take on this puzzle?
Whats your take on this puzzle?
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Re: The frog riddle
There is not enough information provided to solve the puzzle. We would need a model for the social behavior of frogs, to determine the probability that a pair of frogs found together would have each possible combination of genders, as well as the probability that a lone frog would be male or female.
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 Eebster the Great
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Re: The frog riddle
As a probability puzzle, it is pretty straightforward and the narrator does a decent job of explaining it. Qaanol, the narrator says that each frog's sex is independent.
 gmalivuk
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Re: The frog riddle
blademan9999 wrote:https://www.youtube.com/watch?v=cpwSGsbrTs
Whats your take on this puzzle?
I don't understand what or why you're asking. The video explains how the puzzle works.
Do you disagree with the explanation? Do you want someone here to help you understand it? Do you just want to know whether we think it's a good puzzle?
Re: The frog riddle
*sigh* that's not how conditional probability works.
Just like the endless misunderstandings of the monty hall problem, this one depends on a hidden question: What's making the frog croak?
You gained some information, but how did you gain it, and how likely were you to gain exactly this information in each possible starting configuration?
The monty hall problem only works if the host has knowledge of the doors, and is bound by the rules of the game show to always reveal one door with a goat. Say you pick door A, and the host reveals door B. The chance for revealing door B when the price is behind door B is 0%, when it's behind door C it's 100%, and when it's behind door A it's 50%. Do the math, then pick door C.
The information "B is a goat" will only ever increase your odds to 1/2. Two doors left, same chance for each. The crucial information is "the host chose to reveal door B", which has different likelihoods in different starting configurations.
Same here. We've established that the frog's genders are independent for this riddle. If you pick one of the two frogs and you tickle it until it croaks, then that croak is not going to tell you anything at all about the gender of the other. That's the definition of independent events.
If by decree of the wood fairy exactly one of the two frogs is required to reveal its gender during the riddle, then you need to include that event in your conditional probability. Realize that hearing a male gender reveal is more likely when there are two males, and when weighting the configurations accordingly, your conditional probability P(one frog is female  one frog is revealed as male) is exactly 0.5. Again, no information about a single frog will tell you anything about the other.
If there's a game show host who has knowledge of *both* frogs, and who's required to tell you either "there's at least one male frog" or "they're both female", then after hearing the first statement you can correctly expect a 2/3 chance for a female.
(Remember: this is bad news, because two frogs otherwise have a 75% chance for one female, and now you're down to 66%.)
tl;dr: the video refuses to give a crucial piece of information. The given answer is thus neither correct nor false; it's meaningless.
Just like the endless misunderstandings of the monty hall problem, this one depends on a hidden question: What's making the frog croak?
You gained some information, but how did you gain it, and how likely were you to gain exactly this information in each possible starting configuration?
The monty hall problem only works if the host has knowledge of the doors, and is bound by the rules of the game show to always reveal one door with a goat. Say you pick door A, and the host reveals door B. The chance for revealing door B when the price is behind door B is 0%, when it's behind door C it's 100%, and when it's behind door A it's 50%. Do the math, then pick door C.
The information "B is a goat" will only ever increase your odds to 1/2. Two doors left, same chance for each. The crucial information is "the host chose to reveal door B", which has different likelihoods in different starting configurations.
Same here. We've established that the frog's genders are independent for this riddle. If you pick one of the two frogs and you tickle it until it croaks, then that croak is not going to tell you anything at all about the gender of the other. That's the definition of independent events.
If by decree of the wood fairy exactly one of the two frogs is required to reveal its gender during the riddle, then you need to include that event in your conditional probability. Realize that hearing a male gender reveal is more likely when there are two males, and when weighting the configurations accordingly, your conditional probability P(one frog is female  one frog is revealed as male) is exactly 0.5. Again, no information about a single frog will tell you anything about the other.
If there's a game show host who has knowledge of *both* frogs, and who's required to tell you either "there's at least one male frog" or "they're both female", then after hearing the first statement you can correctly expect a 2/3 chance for a female.
(Remember: this is bad news, because two frogs otherwise have a 75% chance for one female, and now you're down to 66%.)
tl;dr: the video refuses to give a crucial piece of information. The given answer is thus neither correct nor false; it's meaningless.
 gmalivuk
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Re: The frog riddle
But then by your account conditional probability is never usable because there's always additional unknown information that would further change the likelihood of different things happening.
The point the video shows, correctly, is that the knowledge that at least one is male (not that a particular one is male, which is what your tickling scenario would show) should change your estimate of the likelihood that they're both male.
The point the video shows, correctly, is that the knowledge that at least one is male (not that a particular one is male, which is what your tickling scenario would show) should change your estimate of the likelihood that they're both male.
Re: The frog riddle
gmalivuk wrote:But then by your account conditional probability is never usable[...]
So the idea that I cannot account for every small factor means that I get to ignore the big factors without having to care about confidence or error bars?
gmalivuk wrote:The point the video shows, correctly, is that the knowledge that at least one is male (not that a particular one is male, which is what your tickling scenario would show) should change your estimate of the likelihood that they're both male.
The information you're getting is not "at least one of them is male" (which I agree yields 2/3, per my third scenario), but "one of them croaked", which allows for different valid interpretations. In a set of independent variables, revealing one variable cannot give you information about the others, no matter if you reveal a specific variable or you pick a variable to reveal at random. And, as worded, this sounds a lot like revealing a single variable.
Both Monty Hall and Betrand's paradox teach us to be precise about these things, because they matter. If the riddle can't be precise about them, the riddle doesn't get to claim a precise answer. It certainly doesn't get to claim that 50% is obviously wrong.
This could have been avoided with a proper setup, for example: "You know that any time two female frogs meet, they both start croaking. These two are silent." Now it's knowledge of the twofrog system and not of a single frog, 2/3 is the only correct answer, good riddle.
 Eebster the Great
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Re: The frog riddle
I will grant that from a practical standpoint, the problem doesn't really work. If male frogs always croak, then we already know the noncroaking frogs are female. If male frogs sometimes croak and sometimes don't, then a pair of males is more likely to produce at least one croak in the given interval than a single male. Croaking frogs are not the ideal setup.
However, we can make a pretty minor adjustment so it works. Instead of croaking, males reveal their presence through a distinctive scent. Unfortunately, there is no way for the human nose to reliably tell the difference between the scent of just one male and of two males. Moreover, the wind is blowing such that you can only pick up smells from the direction of the clearing, not the stump. Now in this scenario, still assuming normal stuff like that the sexes are all independent, the problem should work properly.
The thing is, the video is obviously not about frogs. It's about conditional probability. And its description of how conditional probability works here is correct.
However, we can make a pretty minor adjustment so it works. Instead of croaking, males reveal their presence through a distinctive scent. Unfortunately, there is no way for the human nose to reliably tell the difference between the scent of just one male and of two males. Moreover, the wind is blowing such that you can only pick up smells from the direction of the clearing, not the stump. Now in this scenario, still assuming normal stuff like that the sexes are all independent, the problem should work properly.
The thing is, the video is obviously not about frogs. It's about conditional probability. And its description of how conditional probability works here is correct.
Re: The frog riddle
I didn't watch the video, so I'm not 100% certain of the details of this frog riddle, but it sounds like it's closely related to the Boy or Girl Paradox.
Re: The frog riddle
Yes, it is. The video's scenario makes it a bit harder to accept the answer because of the reasons given so far.
Surely the frog croaks loudly because it's calling for a female, so the one next to it must be another male.
Surely the frog croaks loudly because it's calling for a female, so the one next to it must be another male.
Re: The frog riddle
Males of many species are also known to make loud calls after successfully mating though. Exhibit A.
 gmalivuk
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Re: The frog riddle
Tub wrote:gmalivuk wrote:But then by your account conditional probability is never usable[...]
So the idea that I cannot account for every small factor means that I get to ignore the big factors without having to care about confidence or error bars?
Then call it confidence rather than probability if you like. There's a sense in which that's already what we're talking about whenever the thing under consideration has already happened.
These nitpicky objections always come up in conditional probability but rarely in "simple" probability, which makes them tend to feel disingenuous.
If you see one frog to your right and two to your left, which direction is more likely to have the female that saves you? For some reason almost no one ever objects to the claim that the pair is the safer bet even though you're still missing information that could totally change the relative odds. Maybe these are Alex Jones's frogs and all the males have been turned gay, so males all go around in pairs and females are mateless and solitary.
Re: The frog riddle
Eebster the Great wrote:As a probability puzzle, it is pretty straightforward and the narrator does a decent job of explaining it. Qaanol, the narrator says that each frog's sex is independent.
No, the narrator’s statement of the puzzle does not say that. It does say that male and female frogs occur in equal numbers, but it does not make any claim about independence.
The only time anything is mentioned as independent is during one of the examples of an incorrect answer, which is not part of the statement of the puzzle.
And it certainly matters, since one could easily imagine a species where individuals always live alone except when they pair up to mate, in which case the two frogs together would definitely include a female.
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Re: The frog riddle
It looks like you're right, he mentions it later in the video. I think the fact that it's an idealized problem is pretty clear from the outset though, even if not every assumption is stated explicitly.
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