Frog probability

[Aractus]

No. I already broke it down for you. Both the videos are wrong in their assessment of the probabilities, however I did explain that the TED-Ed video is "almost right" since their assessment of the probabilities would be correct if there was an exactly 50% likelihood for a male frog to croak while you are there. But since that is an unknown variable it's likely that the exact probability is different.

So, imagine a space of 400 randomised pairs of frogs. In total you had 400 male frogs, and 400 female frogs, and allowed them to pair up randomly. By doing this you would expect about 100 male-male pairs, and about 100 female-female pairs, and about 200 pairs with both a male and a female. It won't be exactly 200, there'll be some random variance - but 200 the number you expect from chance. Now out of your 400 pairs, you select one pair at random. The probability of it being male-male is 1/4, female-female is 1/4 and male-female/female-male is 1/2. So it's equally likely to get a pair of the same gender or a pair with each gender. Next you learn that your pair contains a male through random chance. This means it can't be a female-female pair, so they are removed from your original sample space of 400. You new sample space is 300 pairs, in which about 100 are male-male, and about 200 are male-female pairs. Thus it's twice as likely that your pair contains a female than for it to contain a pair of males.

However, as I discussed the probability of croaking changes the results. If croaking is less likely then a male-male pair becomes more likely, however it is never going ot be as much as 50%. As the chances of croaking increase, the chances of it being a boy-girl pair also increase due to you not hearing the other boy frog croak.