KV,
Might be a monkey too ( just joking ).
The way I look at it Woof has just used the family as an example.
The real question is you have a 50/50 scenario and one half of the 50 has gone so we should be left with the other 50 being 100%, but I could be wrong.
Woof could you PLEASE give us the answer, I can't eat or sleep and I am having nightmares ( they are the ones that race at Mooney Valley at night ) about this.

50% chance.

Chance has no memory.

So what's the chance that the family has two girls, and what's the chance it has two boys???

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Each time at the well produces a 50/50 chance. one sperm in a billion getting through. However if the sire has allready produced one girl the likelihood of a repeat is higher than that of producing a boy. Atheletic types have a higher temperature and predominantly produce girls. There is all sorts of other criteria which may slightly change the odds.

A bit like horse racing.

Besides that I hope everybody had a good Christmas and has a prosperous New Year

Clearly 50%. The fact that there is a girl is just there to throw people off. It is irrelevant.



Here is the answer.

Well, an interesting set of answers.
Here is the correct one:
2/3 or .667 -- the probability that the family also has a boy is 2/3. (cheers jfc)
And here's the logic:
You were told a family has two children. There are four possible ways in which a family can have two children:
#1 Girl-Girl (probability = .25)
#2 Girl-Boy (prob = .25)
#3 Boy-Girl (prob = .25)
#4 Boy-Boy (prob = .25)
Each of those four ways of having two children has an equal probability of happening, and those probabilities, of course, add up to 1.000. (as specified in the question: Assuming that the biological probability of having either a boy or a girl baby is equal 50-50).
You were told that one of the children was a girl. That only eliminates one possibility out of the four: Boy-Boy, leaving three other possibilities, (GG, GB, BG) all of equal probability. Of those three, two include a boy. Thus the probability that the family ALSO has a boy is 2/3 or .667.
The most common mistake that people make when confronted with this problem is that they try to reduce it to a simpler problem. The mistake is in thinking that the FIRST child was a girl, so what is the probability that the SECOND child is a boy. In that improperly simplified problem, you have eliminated TWO out of the four possible ways of having two children (Boy-Girl and Boy-Boy) leaving only two possibiliities, only one of which has a boy in it. And thus the mistaken 50% answer. The mistake was in eliminating Boy-Girl from the set of possible situations during the simplification.

thank you

OK. I think I misread the question. My thinking was that they were expecting another, what were the chances. I think that I missed the obvious wording of the question implying that the child was already born.
All makes sense now.

I presume that those of us that said 50% would be right provided that we were guessing the sex of the second unborn child?

I'm with you on that BJ, I must of read the question the same way you did, basing my answer on the thinking the second child was yet to be born, but I should have given it a bit more thought. I always seem to rush in without thinking things through clearly.

Beton, My offspring in order are Boy Girl Boy. If I was at my athletic peak when producing the girl then I must have been in pretty bad shape when producing the Boys.

At the risk of being seen as a bad loser (or looser in some circles) I consider this a badly worded question. Just the sort of question a study of statistics is likely to engender as we all know statisticians like their figures to mean what the statistician wants them to mean.

Scenario 1. A family has two children and one of them is a girl therefore it is logical to assume one of them isn't. I mean how many non statisticians would say "I have two children, one is a girl and the other is a girl."
So: Answer to the original question 100%

Scenario 2. We see a picture of the unfortunate statisticians children, they aren't attractive, in fact you can't tell what sex they are with their clothes on. The statistician points to one and says 'She is a girl'. What's the other one then we wonder and of course the answer is 50/50 it's a boy since it's a even chance either way.
So: Answer to the original question 50%

The 66% scenario is more of a play on words than a sensible question.

Well, someones gotta be controversial. Crash has dissappeared and P57 has a fortnight in the sin bin.

KV

and P57 has a fortnight in the sin bin.

KV[/QUOTE]
No wonder the longshot thread is slipping down the pecking order!!

p.s could someone please tell me how to quote only part of a post? I highlighted part of the quote but the whole thing appeared on my reply anyway.

KV
The whole point about playing our handicapping game (and a lot of the "game of life") is being forced to make decisions even when faced with incomplete or conflicting information. And a person that is better at determining those probabilities and expectations in the handicapping domain, especially with uncertain information, gets paid more money in the long haul.

Thus a person that wants to progress in the game of handicapping has to first become reasonably proficient in probability and statistics, and then move on to heuristics and biases and the study of a couple or three aspects of psychology. We're all peeling the handicapping onion so to speak!