Ted-Ed Frog Riddle Solution
If likelihood of male frog croaking at any point in time is 1/1
Boy & Boy
P (croaks + no female)
silent
Boy & Girl
P (croaks + has female)
silent
Girl & Boy
P (croaks + has female)
silent
Girl & Girl
silent
P (has girl | croak)
= \( P (\ has\ girl\ \cap\ croak ) \
\over P (croak) \)
= 2/3
or
66.7%
Girl
P (silent + has female)
Boy
croaks
P(silent + no female)
P (has girl | silent)
= \( P (\ has\ girl\ \cap\ silent ) \
\over P (silent) \)
= 1/1
or
100.0%
Best direction to run: Right
Explanation:
We make a model such that at any point in time, there is a certain probability, 1/1, that
male frogs croak.
Using Bayes' rule, we can calculate 2 probabilities:
(1) Given that you heard a croak from the left, what is the probability that the left-side croak comes from a male-female pair?
(2) Given that it was silent on the right side, what is the probability that the silence comes from a female?
Using Bayes' rule, we can calculate 2 probabilities:
(1) Given that you heard a croak from the left, what is the probability that the left-side croak comes from a male-female pair?
(2) Given that it was silent on the right side, what is the probability that the silence comes from a female?
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