Skip to main content

Can you solve the frog riddle? - Derek Abbott

8,385,264 Views

18,227 Questions Answered

TEDEd Animation

Let’s Begin…

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.

About TED-Ed Animations

TED-Ed Animations feature the words and ideas of educators brought to life by professional animators. Are you an educator or animator interested in creating a TED-Ed Animation? Nominate yourself here »

Meet The Creators

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

The answer is "go to the stump" and here is why

duckware.com/tedfrog has a very detailed explanation as to why, including a working simulation to play around with! Set the probability that a frog croaks to 'p' (a variable). That then defines a full sample space, and once filtered using the condition specified in the riddle (heard a male croak from clearing) you get a new sample space. The probability of finding a female frog in that new space in the clearing is the SAME formula as the probability of finding a female frog on the stump. Therefore, since your "chances of survival" are equal no matter which way you go (regardless of croak probability), and you are getting ready to "collapse", it is more prudent to take the time to lick one frog (not two). So go the stump!

Comments are closed on this discussion.

Avatar for Ashok Kimmel
Lesson in progress

In my opinion, the simplest thing to do is to use a tree diagram.
There are two possibilities for the left. Then it can be substituted more.
You heard the right. You heard the left.
The left is male It is female. Right is male. It is female.
If all of those are equally likely the probability is 50%. The stump is also fifty percent. Therefore go to the stump.

More from Math In Real Life