http://www.perlmonks.org/?node_id=796576

and

“There is an empty house. Two mothers and two daughters walk in. The house catches fire! Three people escape in time. The house burns down, and noone was hurt. How is this possible?”

So while I agree that gender bias is real and present in life, not all math problems are about Fathers and Sons. (Sorry, Turgenev.)

P(GG|At least one is a girl, born on a tuesday) is 13/27

Infact P(GG|At least one is a girl, with a further 1 in n restrction) is 2n-1/4n-1

I have rather an interesting article I wrote last year on this problem. If people want it, I can email it/post it here

I just posted a blog/video post on the basics of probability, but your post is definitely several steps beyond basic.

Thanks for sharing!

http://blog.thinkwell.com/2010/08/7th-grade-math-probability.html

I’ll shut up now.

With regard to which is more probable (Tanya’s post of 9 April): 1. That you started writing about Tues and then discovered that you had a son born on Tues, or 2. You started writing about Wed then checked that you had a son born on Tues and changed your essay to Tues:-

This depends on whether you would change to Tues if you had a Tues boy, even if you also had a boy of the type you were first writing about (Wed).

If you were going to change to the Tues spec wherever possible, then I would have thought that Cases 1 and 2 are equally probable. This is if you are just considering Wed. If you mean all days other than Tues, then Case 2 is 6 times as likely as Case 1.

However, if you were only going to change to Tues if you did not have a Wed boy, then the chances of having a Wed boy being (1/7 + 1/7 + 13/49) divided by 3 = 9/49(?), the probability of changing to the Tues spec would be 40/49 instead of 1. If this type of change applies to all non-Tues days, then the chances of changing to Tues would be 40/49 x 6 = 240/49, i.e. about 5 times instead of 6. I don’t think there should be a reduction as I don’t think any double counting has gone on, but I’m not at all sure.

In conclusion, considering Wed only, Cases 1 and 2 are equally probable if you change to the Tues spec wherever possible, but Case 1 is more likely by about 1/5 (I don’t know how to work it out exactly!) if you only change when you don’t have a Boy Wed. And if you are considering all non-Tues days, then Case 2 is 6 times more probable than Case 1 in the ‘change whenever possible’ scenario, and about 5 times more probable in the latter scenario.

This is all assuming that you would DEFINITELY change if you had a Tues boy and didn’t have a boy of the day you were writing.

This is probably all wrong.

Of course, you might be lying (with good reason: it makes a good problem), but I think one has to discount this fact as the puzzle would not make sense. You certainly couldn’t take any bets on it.

However, I’m having trouble with your cat-amongst-the-pigeons post of 9 April (sorry - I’ve only seen this website today). I had thought this puzzle had originated elsewhere with the Tues spec and therefore you would be unlikely to have changed it to (WLOG) a Wed spec unless you actually had such a boy. I suppose you could then have changed it back again to Tues if you later discovered that your other boy was born on a Tues, in which case the chances of having 2 boys is 1.

But assuming for the moment that you did start arbitrarily with BoyW and then found at least one of your children was in fact a boy born on Tues, and so changed the puzzle to the BoyT spec, then I think the chances of you having 2 boys goes down from 13/27 to 11/25 as the BoyT/BoyNotT and BoyNotT/BoyT categories change to BoyT/BoyNotTorW and BoyNotTorW/BoyT - i.e. from 12 perms to 10 perms.

This is a different answer to Bill’s 3/10, and as he’s a mathematician and I’m not, he is likely to be right. But where is my mistake?

Traditionally ‘he’ can be either ‘he’ or ’she’ in legal docs etc, as ‘man’ in the human sense includes ‘woman’. So we are slightly indoctrinated to talk about a boy rather than a girl. To mention a girl instead would seem to be a little feminist.

However, I feel the parent should be a woman rather than a man. Apart from the traditional role women have with children, it makes life easier when one knows that when one refers to ‘he’ one is talking about the child, and that ’she’ refers to the parent.

But possibly most mathematicians are men (?) - I don’t know this (I’m not one) - so they would pose the problem from their viewpoint.