To math it out more:
chance of mm with one male croaking: x+y
chance of mf croaking: w (Since the change of a male croaking may be reliant on the presence of a female)
chance of lone male not croaking: z
Where none of these variables are related without assumptions.
So guess what, your problem, which intended to fool others only fooled yourself.
No, because x for male 1 != x for male frog 2. You'd have to make an assumption that x is constant across all male frogs. You didn't even say all male frogs croak, you just said only male frogs croak. Only men have gone to the moon, that does not mean all men go to the moon.
>Wrong. Since we heard a male croak the probability is nonzero.
Wrong since we don't know it's a constant probability.
>It literally does. Since females never croak while males sometimes croak, a non-croaking frog is always more likely to be female.
We do not know that all males croak, only that some males croak. Therefore the probability that it is a male AND croaks decreases, but the probability that it is a male does not decrease.
>This simply proves it is possible to not hear a male frog croak. But we are talking about the probability of male vs. female. Females never croak and there female is more likely.
Not if the probability of all males except that one male that croaked is 0, which is totally possible. Maybe this male had a mutation and he's the only male who croaks.
>No I did not. I specifically said that x is the chance of a make frog croaking, not a rate. This chance exists regardless of the variability in rates across the frog population.
Sorry, should have written, "You've just made an assumption that all males have the same chance of croaking"