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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by Hugh O'Byrne
Hugh O'Byrne
Lesson in progress
New candidate answer: 9/14
Assuming the calculations are made at the instant the first croak is heard, and it's from the pair of frogs, (and some more assumptions that won't fit in this space): (X0 to left, X1X2 to right) F0F1F2: No croak. probability 1/8 (A) F0F1M2: First croak from right: 1/8 (B) F0M1F2: First croak from right: 1/8 (C) F0M1M2: First croak from right: 1/8 (D) M0F1F2: First croak from left: 1/8 (E) M0F1M2: First croak from left: 1/8*1/2=1/16 (F) M0F1M2: First croak from right: 1/8*1/2=1/16 (G) M0M1F2: First croak from left: 1/8*1/2=1/16 (H) M0M1F2: First croak from right: 1/8*1/2=1/16 (I) M0M1M2: First croak from left: 1/8*1/3=1/24 (J) M0M1M2: First croak from right: 1/8*2/3=1/12 (K) (B+C+G+I)/(B+C+G+I+D+K) = 9/14.
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Hugh O'Byrne
Hugh O'Byrne
Lesson in progress
in response to Brady Printer Show comment
I'm not sure what you mean by 'that'.
When I say, "new candidate answer", I mean that in addition to the answers 2/3 and 1/2, I am adding 9/14 to the set of values to be considered as an answer to the question. I disagree with the 'order doesn't matter' justification for the answer 1/2, because it's just false, and I disagree with the 2/3 answer because there's no reason the victim shouldn't be able to hear as well from one direction as from the other.
If you're asking about (B+C+G+I)/(B+C+G+I+D+K), the events B, C, G, and I are those that match the story (first croak is heard from the right) where the victim survives by going to the right (one of the pair is female), and D and K match the story but the victim dies if he goes to the right (both are male).
If you mean something else, please tell me what 'that' means.
Brady Printer
Lesson in progress
what does that mean?
Hugh O'Byrne
Hugh O'Byrne
Lesson in progress
I think there's actually one more important assumption I'm making: that the pair of frogs is seen immediately upon hearing the croak. (Apologies for the disjointedness, I'm still working through some of the details myself.)
Hugh O'Byrne
Hugh O'Byrne
Lesson in progress
To clarify some of the extra assumptions.
The combinations F0F1F2, F0F1M2, F0M1F2, F0M1M2, M0F1F2, M0F1M2, M0M1F2, M0M1M2 are all equally likely. This does not strictly follow from what is stated in the video, that there are an equal number of male and female frogs. For instance, it could be that there are precisely 2 male frogs and 2 female frogs in the world, and then, the combinations above are certainly not equally likely (F0F1F2 and M0M1M2 are impossible).
Given that there is one male to the left and one male to the right, the first croak you hear is equally likely to come from either direction. Given that there is one male to the left and two males to the right, it is twice as likely the first croak you hear will come from the right.
There was no croak heard from the left at the time he makes this calculation (if there was, he wouldn't be shown hesitating which direction to pick).
