Frog probability

[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%.