Can You Solve the Frog Riddle?

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In this riddle from TED-Ed, you're in a sticky situation. You're stranded in a rainforest and have accidentally eaten a poisonous mushroom. To survive the poison, you need to lick a very particular frog. But which frog is it?

You can watch the video below for more details, or read this description. The problem is simple: You are poisoned and you know that a particular species of frog produces the antidote, which will cure you if you lick it. But to make things more complex, you know that only female frogs of the species have the antidote—males do not. In this frog species, males and females look identical but males have a distinctive croak. (Males and females also occur in identical proportion in this species.) In one direction, you see a single frog. In another, a group of two frogs sitting together.

From the direction of the two frogs, you hear that distinctive "male frog" croak. Uh-oh! One of those two is definitely male.

As the poison sets in, you have to make a logical decision. You need to find a female frog with the antidote. Are your odds better going toward the group of two (one of which is definitely male), or toward the single unknown frog? And what are those odds, anyway?

Note that in this riddle you are not guaranteed to survive. You're just trying to take your best shot.

So which to choose, and why?

Watch the video below for a discussion of the problem and how the math stacks up behind one of the choices.

For more resources, consult this TED-Ed page. Once you've solved it (or if you've given up), you might also be interested in this related math problem.