Can you solve the frog riddle?

boing
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But then, thinking about it, how many programmers would ever find themselves on the banks of a river with a canoe, a leopard, a goat and a cabbage?

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These west African frogs have been known to spontaneously change sex from female to male.[2] This likely occurs when the population does not have enough males to allow procreation and is accomplished when a chemical trigger activates the sex gene to disintegrate the female organs and develop the male ones.

Maybe you’re just fucked.

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Unless you just doubled down on ludicrous replies I think I’ll just anthropomorphically hop away from this conversation before one of us croaks the big sexy.

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I don’t agree with the explanation, I think. When you first see the two frogs, one of them already is a 100% male. The fact that you don’t know that, doesn’t change this. And then you hear the croak. So from that moment you know: I see one male frog, and one frog with an unknown gender. Which is which? That doesn’t matter. One of the frogs has a 100% chance of being male, and the other 50%. So run to the frog on the stump. It’s easier to lick one frog than two.

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And I would like to add: this looks like the famous 3 door problem, but it’s different. With the three doors, there are only… three doors. So if you know something about one door, that influences the chances of the others. In this frog problem, there is an unlimited number of frogs. So if you know that one frog is male, that does not tell you anything about the other frog.

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Using morons for lethal experiments and keeping it quiet, I hope not.
But as far as completely backwards statistical reasoning is concerned, there are plenty of examples.

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This frog puzzle is a bold attempt to update an older, flawed puzzle. The older puzzle was that your friend told you, “My new neighbor has two children. At least one is a boy.” What is the probability that the neighbor’s children are a boy and a girl? The answer is 2/3.

If the friend had instead said, “The older child is a boy,” or “The child I met is a boy,” that changes the probability to 1/2. Once we can concentrate all the information about the two children onto one child, the probability of the other child’s sex goes back to the prior 50:50 odds. The problem with the puzzle is a person saying, “At least one is a boy,” probably means, “The child I met is a boy.”

And in the frog puzzle, the information we have about the pair of frogs is not that at least one is a male. Instead, our information is that the one that croaked is a male. That we lost track of which one croaked does not change the odds.

Consider the sample space diagram at time 2:45 in the video: four rows representing the possibilities: (male,female), (male,male), (female,female), and (female,male). The narrator eliminates (female,female) because female frogs don’t croak. But let us add some more information: label the left column “Croaked” and the right column “Silent.” That means that we also have to eliminate the (female,male) case, too. The chance of having a female frog in the pair is only 50%.

I performed a full conditional probability calculation using Bayes’ Theorem to check my conclusion. It revealed a critical unknown factor, p, the probability that a male frog would croak during time of the poisoned character’s search. The chance that the frog on the stump is female is 1/(2-p). The longer it stayed silent against the odds of a male frog croaking, the more likely it was female. And the chance that the pair of frogs contains a female is also 1/(2-p).

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