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
Gustavo Cervantes
Lesson in progress
(58%) The additional information could also raise the probability of the single frog being female.
How?If we assume the frogs come from the same sample space and not from two independent samples, the fact that there is already a male within the three frogs affects the probability of both choices Combinations: 1.MM,F 2.MF,F 3.FM,F 4.FF,F 5.MM,M 6.MF,M 7.FM,M 8.FF,M One of the frogs in the clearing is male.This rules out numbers 4 and 8. Six possible combinations with two options each are left, e.g., if we get combination number one and choose the clearing,we die; the tree trunk,we live. 12 options out of six combinations, 7 that result in us getting a female frog. This makes our chances of survival 7/12. Hence, the tree stump option is raised around 8% by the additional information giving us a 58% chance of getting a female.
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Gustavo Cervantes
Lesson in progress
in response to Gustavo Cervantes Show comment
Just to clarify, the option of the clearing is still a better choice. It is now a matter of choosing between 7/12 in the tree stump and 2/3 in the clearing.
I think the video could have been better if the additional information would have affected the two options.
Gustavo Cervantes
Lesson in progress
in response to Hugh O'Byrne Show comment
I'm just saying that the frog on the tree stump would also be affected by the fact that you know there is a male frog in the clearing if it belongs to the same sample space as the frog on the tree stump.
If the frogs belong to the same sample, having a male affects the probability of all the other unknown gender frogs you may find from the sample. In other words, out of the 2/3 chances of survival that you would get if you find only two frogs, your chances would get equally distributed between any additional frogs you find (unless the additional frogs you may find would belong to a different sample source).
So, when you find three frogs, the probability of the unknown frogs of being female gets distributed. 1/12 out of the 2/3 chances goes to the third frog.
This is what happens then, you find a single frog and you have 1/2 chances. You then find the other two frogs, male and unknown, and this additional information changes the probability of the first frog by raising it to 7/12
Hugh O'Byrne
Hugh O'Byrne
Lesson in progress
You seem to be answering the question, if the victim randomly chooses between the clearing and stump (50/50), what is the probability of survival?
That is not the question asked by the video.
