Frog probability

[Jackalope]

No.  A single croak only means that there is necessarily at least one male.

Yes, that's what I'm saying. A single croak meaning a single male frog implies a double croak meaning two frogs.
How do you know there were two frogs and they croaked simultaneously making it sound like a single croak?

You completely missed the point.

Males can croak. Females can not. That doesn't mean that males *must* croak, only that they *can*. A non-croaking frog is of indeterminate sex.

[ErGingerbreadMandude]

Yes, that's what I'm saying. A single croak meaning a single male frog implies a double croak meaning two frogs.
How do you know there were two frogs and they croaked simultaneously making it sound like a single croak?

You completely missed the point.

Males can croak. Females can not. That doesn't mean that males *must* croak, only that they *can*. A non-croaking frog is of indeterminate sex.

Okay so you're saying that there could've been two males and only one decided to croak.
I thought of it like this:

*If there will be a croak there will be a male frog.
*If there is two croak there will be two male frogs.
*If there is only one croak then the other frog is not male.
*If the other frog is not male then it's a female frog.

[bennyboy]

No.  A single croak only means that there is necessarily at least one male.

It means one frog is male.  The other is unknown, and I still don't think that the pairings you guys have shown work-- because they attempt to place samples into ordinal positions which they don't need to have. A frog croaks-- okay it's male. The other one didn't croak-- okay, it's male or female, approx. 50% chance.

[TheRealJoeFish]

No.  A single croak only means that there is necessarily at least one male.

It means one frog is male.  The other is unknown, and I still don't think that the pairings you guys have shown work-- because they attempt to place samples into ordinal positions which they don't need to have.  A frog croaks-- okay it's male.  The other one didn't croak-- okay, it's male or female, approx. 50% chance.

This is one of those questions that's famous because the correct answer is not intuitive (CD's 2/3 is the correct answer, when intuition tells you it's 1/2).

Here's how I'd consider it, without getting into "left sharkfrog right sharkfrog".  You know a frog's 50/50 m/f, and you know there are two of them.  Say they're in a box.  Your box of frogs either has: 2 females, 1 male and 1 female, or 2 males.  We can agree that the probability of 2 females is 25%, the probability of 1/1 is 50%, and the probability of 2 males is 25%, right? That is, it's twice as likely that there's both a male and female than there are two females, and it's twice as likely that there's both a male and a female than there are two males.

But then a croak comes from the box.  That totally gets rid of the first possibility (2 females) because females don't croak.  So, now the possibilities are "male and female" and "male and male", and we know from before that it's twice as likely there's "male and female" than there's "male and male."  So, the first occurs 2/3 of the time.

[Jackalope]

You completely missed the point.

Males can croak.  Females can not.  That doesn't mean that males *must* croak, only that they *can*.  A non-croaking frog is of indeterminate sex.

Okay so you're saying that there could've been two males and only one decided to croak.
I thought of it like this:

*If there will be a croak there will be a male frog.
*If there is two croak there will be two male frogs.
*If there is only one croak then the other frog is not male.
*If the other frog is not male then it's a female frog.

That would kind of completely make this not a puzzle, don't you think?

[Jackalope]

No.  A single croak only means that there is necessarily at least one male.

Yes, that's what I'm saying. A single croak meaning a single male frog implies a double croak meaning two frogs.
How do you know there were two frogs and they croaked simultaneously making it sound like a single croak?

No. You and I are completely NOT saying the same thing, as far as I can see.

[bennyboy]

It means one frog is male.  The other is unknown, and I still don't think that the pairings you guys have shown work-- because they attempt to place samples into ordinal positions which they don't need to have.  A frog croaks-- okay it's male.  The other one didn't croak-- okay, it's male or female, approx. 50% chance.

This is one of those questions that's famous because the correct answer is not intuitive (CD's 2/3 is the correct answer, when intuition tells you it's 1/2).

Here's how I'd consider it, without getting into "left sharkfrog right sharkfrog".  You know a frog's 50/50 m/f, and you know there are two of them.  Say they're in a box.  Your box of frogs either has: 2 females, 1 male and 1 female, or 2 males.  We can agree that the probability of 2 females is 25%, the probability of 1/1 is 50%, and the probability of 2 males is 25%, right? That is, it's twice as likely that there's both a male and female than there are two females, and it's twice as likely that there's both a male and a female than there are two males.

But then a croak comes from the box.  That totally gets rid of the first possibility (2 females) because females don't croak.  So, now the possibilities are "male and female" and "male and male", and we know from before that it's twice as likely there's "male and female" than there's "male and male."  So, the first occurs 2/3 of the time.

I know from history (i.e. statistics classes) that you guys are right.  However, I will continue to argue until I "get it," for my own education.

In the video, the person is beckoned to the pair of frogs BY the croaking sound.  In other words, he approached the pair alreading knowing that one of them must be male.  Therefore, there was never any probability that both frogs were female.  This is different than looking at two frogs and one of them croaks, IMO. (I assume the second video says something like this, but I haven't watched it yet)

Since before considering the problem, it was ALREADY known that one of the two was male, it seems to me only the remaining frog (whichever it is, because we don't know) is actually under consideration.  And the odds for one frog to be male are 50%.

[Aractus]

No. I already broke it down for you. Both the videos are wrong in their assessment of the probabilities, however I did explain that the TED-Ed video is "almost right" since their assessment of the probabilities would be correct if there was an exactly 50% likelihood for a male frog to croak while you are there. But since that is an unknown variable it's likely that the exact probability is different.

So, imagine a space of 400 randomised pairs of frogs. In total you had 400 male frogs, and 400 female frogs, and allowed them to pair up randomly. By doing this you would expect about 100 male-male pairs, and about 100 female-female pairs, and about 200 pairs with both a male and a female. It won't be exactly 200, there'll be some random variance - but 200 the number you expect from chance. Now out of your 400 pairs, you select one pair at random. The probability of it being male-male is 1/4, female-female is 1/4 and male-female/female-male is 1/2. So it's equally likely to get a pair of the same gender or a pair with each gender. Next you learn that your pair contains a male through random chance. This means it can't be a female-female pair, so they are removed from your original sample space of 400. You new sample space is 300 pairs, in which about 100 are male-male, and about 200 are male-female pairs. Thus it's twice as likely that your pair contains a female than for it to contain a pair of males.

However, as I discussed the probability of croaking changes the results. If croaking is less likely then a male-male pair becomes more likely, however it is never going ot be as much as 50%. As the chances of croaking increase, the chances of it being a boy-girl pair also increase due to you not hearing the other boy frog croak.