Here is a TED Ed video about a probability riddle. https://youtu.be/cpwSGsb-rTs

Here is the Mind your Decisions video concerning a flaw in the TED Ed reasoning.
https://youtu.be/go3xtDdsNQM

I concur with MyD. Also, I think that the fact that you have not heard a croak from the original frog means that the chance that it is female is higher than 50%.

dv said:

Here is a TED Ed video about a probability riddle. https://youtu.be/cpwSGsb-rTs

Here is the Mind your Decisions video concerning a flaw in the TED Ed reasoning.
https://youtu.be/go3xtDdsNQM

I concur with MyD. Also, I think that the fact that you have not heard a croak from the original frog means that the chance that it is female is higher than 50%.

What is the difference between a GB and a BG, surely in this instance they should be in the same category? Such a change in this understanding would alter the calculations.

Oh no, not the dreaded the older child is a boy problem again.

Anyway, the second video has an unstated assumption that may not be correct, and a stated assumption with no basis.

The unstated assumption is that the female frog is silent, but it may also have a distinctive croak. We are told that the male frog has a distinctive croak because that is what we hear.

The assumption with no basis is that croak and no-croak (over the given time period) are equally likely. The best we can do is knowing that from a group of three with at least one male there was one croak the average croaks per male would be higher than 50%.

I’ll have to have a think about how much higher.

The Rev Dodgson said:

The unstated assumption is that the female frog is silent

No, unstated fact.
Female frogs do not call during mating season.

He died from mushroom poisoning while the egg head was explaining the probabilities to him.
I only watched the first video and egg head is wrong.
It wouldn’t have mattered which way the deceased went it was still 50%.
It’s a cautionary tale.

Jing Joh said:

The Rev Dodgson said:

The unstated assumption is that the female frog is silent

No, unstated fact.
Female frogs do not call during mating season.

OK, but these things aren’t supposed to need unstated information.

For instance, it may well be that the probability of a pair of frogs being M/F is >> 50% in fact, but the person in the puzzle doesn’t know that.

But I’m currently leaning to the position (ignoring all unstated information) that the probability of one female in the pair is exactly the same as the single frog being female, and that probability is something higher than 50%, depending on the average frequency of male croaks.

The Rev Dodgson said:

Oh no, not the dreaded the older child is a boy problem again.

Anyway, the second video has an unstated assumption that may not be correct, and a stated assumption with no basis.

The unstated assumption is that the female frog is silent, but it may also have a distinctive croak. We are told that the male frog has a distinctive croak because that is what we hear.

The assumption with no basis is that croak and no-croak (over the given time period) are equally likely. The best we can do is knowing that from a group of three with at least one male there was one croak the average croaks per male would be higher than 50%.

I’ll have to have a think about how much higher.

Even if you allow for that, the basic news is still the same: introducing this croaking observation into the picture changes the situation in a way that the TED Ed author doesn’t allow for.

This blog piece gives the maths in more detail
http://mindyourdecisions.com/blog/2016/03/08/ted-eds-frog-riddle-is-not-entirely-correct-game-theory-tuesdays/

dv said:

Even if you allow for that, the basic news is still the same: introducing this croaking observation into the picture changes the situation in a way that the TED Ed author doesn’t allow for.

This blog piece gives the maths in more detail
http://mindyourdecisions.com/blog/2016/03/08/ted-eds-frog-riddle-is-not-entirely-correct-game-theory-tuesdays/

I agree that the probability of 1 female in the pair is the same as the probability that the single frog is female.

Possibly coincidentally, I think that probability is 2/3, which is the number given by TED for the pair.

I’ll have a look at the link.

The Rev Dodgson said:

dv said:

Even if you allow for that, the basic news is still the same: introducing this croaking observation into the picture changes the situation in a way that the TED Ed author doesn’t allow for.

This blog piece gives the maths in more detail
http://mindyourdecisions.com/blog/2016/03/08/ted-eds-frog-riddle-is-not-entirely-correct-game-theory-tuesdays/

I agree that the probability of 1 female in the pair is the same as the probability that the single frog is female.

Possibly coincidentally, I think that probability is 2/3, which is the number given by TED for the pair.

I’ll have a look at the link.

OK, the statement that the single frog has only a 50% chance of being female is clearly wrong.

I’ll have to come back to the boys on Tuesday thing.