Can you solve the frog riddle? - Derek Abbott
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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.
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- Educator Derek Abbott
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by TED-Ed
You see two frogs. We tell you the frog on the left is male. What is the probability that the frog on the right is female? Can you explain in your own words why information about a male frog increases your chances of the other being female?
The clever surprising twist in this problem is that you get information about a male frog and yet this increases your chances of the other being a female frog! This is something that can even surprise or fool a trained mathematician until he or she sits down and carefully works it out. So if this is messing with your mind right now, don’t worry as you are in very good company.
Comments are closed on this discussion.
Marcell McClure Baker
Lesson completed
in response to William Thomas Show comment
********** you
Ashok Kimmel
Lesson in progress
in response to Angelo Theoharis Show comment
Well, beyond a certain point, it does not matter. If there are 10,000,000 frogs with half female and half male, very little would change.
William Thomas
Lesson completed
The probability will not change because there are chances that they are both male.
Austin Gowin
Lesson completed
It increases because if there are a equal number of both genders it means you know that the frog has about 50 % chance of being female.
Martin Marion
Lesson in progress
I can explain in my own words that knowing the gender of one of the wrongs in no way impacts the gender of the other frog. It's 50%, based on the information we have. You can add as many male frogs as you want, and the chances of the first one being a female is still 50%. And that has nothing to do with the fact that the chances of at least one frog being female is 67%, if there is a pair, and we know that one of them (but not which) is definitely male. If we know which one is male, the other one's chances are, again, 50%. This video is a mess :)
raahim memon
Lesson in progress
One important difference is that in the Monty-Hall problem the behavior of the host is well defined but it is not defined in this quiz. If you would have told me the sex of the frog on the left no matter what, then this information doesn't increase or decrease the probability of the right frog being female.
Angelo Theoharis
Angelo Theoharis
Lesson completed
If the frog on the right is a male then there is a better chance the other is a female.
If 50 out of 100 frogs are male and 50 are female and knowing the one on the left is male that leaves us with 49 males and 50 females. So there is a slightly higher chance that the one on the right is female.
Yuan Zhang
Lesson in progress
in response to Wayne Matheson Show comment
Clear logic, impeccable proofs and effective presentation. One of the best and simplest explanations on probability.
Wayne Matheson
Wayne Matheson
Lesson in progress
Like others I think this puzzle is just wrong. Two proofs:
The initial dataset it not 2x2 it is 3x3 since the possible states of frog are (f)emale, non croaking (m)ale and croaking (M)ale, so [ff,fm,fM,mf,mm,mM,Mf,Mm,MM]. We can eliminate all conditions where there isn't exactly one M. This leaves [fM,mM,Mf,Mm]. 50% of the conditions include a female.
More simply, since the quantum mechanics theory of observing a frog croaking changing the sex of a nearby frog has yet to be proven. If you see which frog croaks or you don't, the frogs are the same and the possibilities are as well. So if the left frog croaks with the TED-ed dataset or the nine element dataset, the only remaining options are mf or mm. Again a 50:50 option.
Yuan Zhang
Lesson in progress
in response to Julia DeFranco Show comment
Yes, I could see the riddle takes a turn from mathematics to philosophy and then to psychology. The discussions turned out to be more spectacular than the riddle itself, and I couldn't help to associate the riddle with that piece of magic mushroom.
