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Can you solve the frog riddle? - Derek Abbott

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You’re stranded in a rainforest, and you’ve eaten a poisonous mushroom. To save your life, you need an antidote excreted by a certain species of frog. Unfortunately, only the female frog produces the antidote. The male and female look identical, but the male frog has a distinctive croak. Derek Abbott shows how to use conditional probability to make sure you lick the right frog and get out alive.

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Meet The Creators

  • Educator Derek Abbott
  • Script Editor Alex Gendler
  • Director Outis
  • Narrator Addison Anderson
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Avatar for Aleksandr Kupriianov
Lesson in progress

The answer is not 50% even for the single frog. The answer highly depends on the conditional probability of croacking if the frog is male. No paradoxes, there probability is the same for all three cases: when one frog is silent, when we have two frogs and hear exactly one sound (but don't see frogs) and when we have two frogs and see which frog makes sound. The mistake is made in the picture, where option "female/female" disappears after a sound, and options "male/male", "male/female", "female/male" are unchanged. In fact, the probability of the rest options decrease non-proportionally.

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