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Society & Culture1 min ago
Sex
165 Answers
Following on from the entertaining Dice and Socks threads earlier this week I've now found the problem about the sex of children.
One version goes: "You know that Mr. Smith has two children and that at least one of them is a boy. What is the probability that both children are boys?"
Thoughts please?
One version goes: "You know that Mr. Smith has two children and that at least one of them is a boy. What is the probability that both children are boys?"
Thoughts please?
Answers
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One version goes: "You know that Mr. Smith has two children and that at least one of them is a boy. What is the probability that both children are boys?"
I can't see how the answer to FF's question is anything other than 50/50.
You are stood with Mr Smith and his son waiting for Mrs Smith to come along with his other child. She will turn up with either a boy or a girl...50/50.
I can't see how the answer to FF's question is anything other than 50/50.
You are stood with Mr Smith and his son waiting for Mrs Smith to come along with his other child. She will turn up with either a boy or a girl...50/50.
Jim- thanks for your analysis. The consensus seems to be for 1/3 with a few preferring 1/2.
Jim- you went for 1/3. I still feel it depends on how we know that 'at least one is a boy'
Suppose all I know initially is that he has two children. I then walk past his house and see a young boy standing at the window in his pyjamas. So now I know at least one of his children is a boy. But that tells me nothing about the sex of the other child- and isn't there pretty much a 50-50 chance of a child being a boy or a girl?
Jim- you went for 1/3. I still feel it depends on how we know that 'at least one is a boy'
Suppose all I know initially is that he has two children. I then walk past his house and see a young boy standing at the window in his pyjamas. So now I know at least one of his children is a boy. But that tells me nothing about the sex of the other child- and isn't there pretty much a 50-50 chance of a child being a boy or a girl?
It's a labelling issue again.
In the manner of the socks solution:
P(B then B) = 1/4
P(B then G) = 1/4
P(G then B) = 1/4
P (G then G) = 1/4
One is a boy, so GG excluded. Order does not matter, so label options as BB = S(ame) and BG/GB = D(ifferent).
Probabilities change* to:
P(B then B) = 1/3
P(B then G) = 1/3
P(G then B) = 1/3
P(D) = P(B then G) + P(G then B) = 1/3 + 1/3 = 2/3.
P(S) = P(B then B) = 1/3.
So it's 1/3 not 2/3
*(The probabilities aren't actually changing but are just rescaled using conditional probabilities.)
In the manner of the socks solution:
P(B then B) = 1/4
P(B then G) = 1/4
P(G then B) = 1/4
P (G then G) = 1/4
One is a boy, so GG excluded. Order does not matter, so label options as BB = S(ame) and BG/GB = D(ifferent).
Probabilities change* to:
P(B then B) = 1/3
P(B then G) = 1/3
P(G then B) = 1/3
P(D) = P(B then G) + P(G then B) = 1/3 + 1/3 = 2/3.
P(S) = P(B then B) = 1/3.
So it's 1/3 not 2/3
*(The probabilities aren't actually changing but are just rescaled using conditional probabilities.)
It does depend on how we know to an extent, but the question implies that we only know that "at least one is a boy". Absent any further information we have to calculate on the basis that it's either Girl/ Boy or Boy/ girl.
Incidentally, the question has excluded the possibility of twins, which probably screws things up yet again as it's more likely to have identical twins than fraternal twins of opposite gender. But, again, we calculate based on the assumption that there were no twins involved, and as long as we state this then the probability is 1/3, not 1/2.
Incidentally, the question has excluded the possibility of twins, which probably screws things up yet again as it's more likely to have identical twins than fraternal twins of opposite gender. But, again, we calculate based on the assumption that there were no twins involved, and as long as we state this then the probability is 1/3, not 1/2.
Is it? Well, there you go. I should perhaps have looked it up -- but anyway the point is that including twins would change the question.
The answer is, anyway, 1/3 IF we assume no twins, that we only know that one is a boy, and that boys and girls are equally likely. All of these are idealised, but in this ideal world the answer is correct.
The answer is, anyway, 1/3 IF we assume no twins, that we only know that one is a boy, and that boys and girls are equally likely. All of these are idealised, but in this ideal world the answer is correct.
