Frog probability

[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.