Question about the famous frog-riddle: https://www.youtube.com/watch?v=cpwSGsb-rTs

What if you can lick only one of the two frogs on the left?

I would say that then your chances of survival are 25%: 50% for choosing the frog that didn't croak, times 50% for that frog having the right gender.

Is this correct? (If so then I should in that case go for the frog on the right)


Each of the cases Male Male, Male Female, Female Male has $1/3$ probability and you have $1/2$ chance in the latter two cases.

Therefore the probability would be $1/3 \times 0 + 1/3 \times 1/2 + 1/3 \times 1/2 = 1/3$.

You should therefore go to the frog on the right with 50 percent chance of being female as you say.

  • $\begingroup$ I don't think so. For example, let's say it is the Male Female case, then which of those two did I lick? $\endgroup$ – GambitSquared Sep 7 '16 at 22:44
  • $\begingroup$ You say you can only lick one, and if you are in the case Male Female, then either of the two frogs are equally likely to be female, hence 50% chance. $\endgroup$ – user353673 Sep 7 '16 at 22:46
  • $\begingroup$ I agree with this answer (I had misunderstood the problem). $\endgroup$ – Bobson Dugnutt Sep 7 '16 at 23:03
  • $\begingroup$ "Each of the cases Male Male, Male Female, Female Male" ​ would have 1/3 probability if the given had been "at least one of the frogs is male". ​ ​ ​ However, the given is "you're startled by the croak of a male frog ...", and ​ Male Male ​ is approximately twice as likely to produce that as either of the other cases on its own. ​ ​ ​ ​ ​ ​ ​ ​ $\endgroup$ – user57159 Sep 27 '16 at 8:03

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