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
by Park Loqi
Park Loqi
Lesson in progress
This is a mis-application of conditional probability
Conditional probability asks "if we know that at least one of the pair is male what is the probability at least one of the pair is female?" This brings the probability from 0.75 (without hearing a male croak) down to 0.5 (with a male croak). That's the correct application of conditional probability. Let's use a parity approach. Here's the sample space: Pair of frogs are same gender Pair of frogs are different gender If we additionally know there's at least one male, we get this: No females One female The error in the video is amplified by scaling the problem up. Consider 100 frogs, where 99 are known to be male. This doesn't create a 100/101 near certainty of a female in there somewhere! This lesson is fatally flawed.
Comments are closed on this discussion.
Yuan Zhang
Lesson in progress
in response to Park Loqi Show comment
Do we really need conditional probability to solve the frog riddle?
Condition: There are only two sexes in the frog species: Male & Female
If one of the two frogs croaked, then one of the two frogs is a male. Why bother to take the male frog into account? Let's focus on the remaining frog.
The possibility of the remaining frog being a female is the same as the frog on the tree stump, 50% of chance being a male and 50% of chance being a female.
Eric Chen
Eric Chen
Lesson in progress
in response to John Price Show comment
What the video fails to show in its probability calculation is that we're actually not looking at gender pairs. We are actually looking at 3 variables. Male frog that croaked (C), male frog that did not croak (M), and female frog (F). What we know for certain one frog is both male and croaked, our possible combinations are:
CM, CF, MC, FC
Our next step is to factor in our survival. Since our survival is based solely on gender of frog and not croakiness and we know that the frog that croaked is male, transitively, we should replace all C's with M's and we get this:
MM, MF, MM, FM
So our chances of survival on both sides are 50%.
John Price
John Price
Lesson in progress
Pairs of same gender == pairs of different gender (in size). This is true, given that if you pick two frogs at random, you will get a same-gender pair 50% of the time, and a mixed-gender pair 50% of the time.
Remove all female-female pairs, since they are no longer in our sample space (we know we have at least one male in our pair given the problem's definition).
We are now left with the same-gender set which is now half the size of the mixed gender set. That is now a 2:1 ratio.
Park Loqi
Park Loqi
Lesson in progress
Conditional probability can be a tricky concept.
