View Full Version : Just when you thought it was safe... Puzzle 2
A couple have two children. One is a boy. How likely is the other to be a girl?
Again, this isn't a trick question: you should assume that any one child is equally likely to be a boy or a girl. Also, it's easier than the last one. :D
2little2late
22-Apr-05, 19:42
Easy! If the other child isn't a boy then it must be a girl.
Easy! If the other child isn't a boy then it must be a girl.
Nope. Well, your statement is literally true, of course, but it's not the answer to the puzzle. Nice one. :D
In a family of two children, the three possible combinations are {BB, GG, BG, GB}. If one child is a boy, the possible combinations are {BB, BG, GB}, therefore the probability of the other child being a boy is a third, or one in three (and not a half as you might expect).
An interesting variation is that if you instead know that of the two children, the older one is a boy, the combinations of children allowed are {BB, BG}, so the probability is the commonsense answer of one half, or one in two (or evens to the gambler).
*giggles* your not talking about my family then it woul be 99.9 percent certain to be a boy!
surely the fact that one is a boy has no relevance to the sex of the other? Unless they are identical twins of course.
In a family of two children, the three possible combinations are {BB, GG, BG, GB}. If one child is a boy, the possible combinations are {BB, BG, GB}, therefore the probability of the other child being a boy is a third, or one in three (and not a half as you might expect).
An interesting variation is that if you instead know that of the two children, the older one is a boy, the combinations of children allowed are {BB, BG}, so the probability is the commonsense answer of one half, or one in two (or evens to the gambler).
Yawn...
This was supposed to be a puzzle, not an exercise in searching the web. The solution above was copied word-for-word from here (http://www.everything2.com/index.pl?node_id=675191). It was obviously copied because of the style of the answer, and also because it didn't (quite) answer the question, namely "how likely is the other to be a girl?"
The solution is correct of course.
Next time, I will make up a puzzle from scratch. I got this one from a friend, and I didn't know it was "out there" all over the place. I guess I should have checked first...
Scotsboy, you are expelled for cheating! :roll: [lol]
:lol: ...........slopes off to stand in the corner :(
surely the fact that one is a boy has no relevance to the sex of the other? Unless they are identical twins of course.
It's all about combinations. If there are two children, and we know nothing about their sexes, then there are four possible combinations:
boy + boy
boy + girl
girl + boy
girl + girl
where the older child is listed first. Clearly, any given chld is equally likely to be a boy or a girl.
However, in this puzzle we are told that one child is a boy, so the girl + girl possibility is ruled out, and we are left with just 3 possibilities:
boy + boy
boy + girl
girl + boy
Also, we are not told whether the boy is the older or younger child, so we must consider all three combinations, which we assume to be equally likely. Since there are two combinations including a girl, but just one including a second boy, then there is a 2/3 chance that the other child is a girl.
There other factors that can infleunce this one though Dr (which are not considered as part of the puzzle.....or are they :confused ) not as cut and dry as the ring in a box.
I am going to show my thick side now. I have more problems understanding DrSzins answers than I do understanding the questions. :confused
How come boy+girl is different from girl+boy?
I am going to show my thick side now. I have more problems understanding DrSzins answers than I do understanding the questions. :confused
How come boy+girl is different from girl+boy?
boy + girl = first-born is boy, second-born is girl
girl + boy = first-born is girl, second-born is boy
They are different combinations and equally likely, so they count as two different possibilities.
boy + boy is a single combination.
Of course, you can tell which boy is which, but that doesn't matter. All we are concerned with here is the number of boys, not whether you can tell one from the other.
And, yes, it's less cut & dried then the ring puzzle. You have to make all sorts of simplifying assumptions, but they are a small effect in practice. Well, that's what most of the stuff on the web claims.
I see. I wasn't thinking along these lines. I was thinking that if some one already had a boy and wanted another child, what are the chances of having a girl.
Im taking the 5th. :confused
Dr S,
In your original question, you said that only one was a boy. That leaves us precious few alternatives for the other. She must be a girl. If not, then was the "couple" to whom you referred cattle perhaps, and the other is a heifer?
:)
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Dr S,
In your original question, you said that only one was a boy.
No I didn't, I said "One is a boy." The "only" is entirely yours.
Quoting me incorrectly is bad enough, but your pedantry is severely misplaced. Saying "One is a boy," does not imply that the other is a girl. Having said that, I will admit that I could have made it a little clearer.
So there! :D
One question:
Does this puzzle take in the possibility of any one of the children being a hermaphrodite?
:)
The question at no point asked about the sex of the other child.
If i am thinking right the chances one of the couple is either male or female is 50/50
why because a one sex couple can now legally adopt children so the chances are 50/50
One question:
Does this puzzle take in the possibility of any one of the children being a hermaphrodite?
:)
i remember when my (then) 8 year old sone asked me what a hermaphrodite was - i have NO idea where he heard the word but i had to go look it up!!!!!
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