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Epyo

I have two kids named Chris...:

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I have two kids named Chris. Chris is a boy. What is the probability that Chris is a boy?

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Epyo said:

I have two kids named Chris. Chris is a boy. What is the probability that Chris is a boy?

Since we know that Chris A is a boy, but nothing about Chris B, it's safe to assume that Chris B is either a boy or a girl. Still, we do not know whether the second Chris mentioned in the question is the same as the first Chris. Thus:
If Chris A is a boy and Chris B is a girl, we have two cases: Chris 1 has to be Chris A, since he is the only boy, but Chris 2 may be either Chris A or Chris B. This would mean there's a 50 % chance so far that Chris 2 is a boy.

Alternatively, both Chrises might be boys. In this case, Chris 1 might be either Chris A or B and Chris 2 might be either Chris A or B. Which ones they are is irrelevant, but still, we have four more cases.

Thus, there are six different cases, only one where Chris 2 is not a boy. Therefor the probability of Chris 2 being a boy is 83.333%


Of course, that doesn't rule out the 50 % chance of you having mental issues and imaginary children.

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All he's saying is that there are two kids named Chris. And "Chris is a boy". Logical reasoning would suggest that both kids are boys. He makes no distiction between either of them anywhere.

He's also not making any distinction when he's asking how large a probability it is that Chris is a boy. For all I can tell, he just told me Chris is a boy in the previous sentence.

So from his way to formulate it, I'd say it's a probability of 1. Or 100%. Though I wouldn't use absolutes so I say 99%.

Unless of course it's a dick move of a riddle which is where it's 50%.

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He also makes no mention of the second "Chris" being a human being. His other "kid" called "Chris" might well be an inanimate object which he cherishes enough to name it as if it were a person and a part of the family (though why it would share the name of his son is admittedly an oddity).

Putting aside the fact that certain languages apply (confusing) sexes to their names of objects, cars and computers and paintings and antique furniture don't actually have the given reproductive organs that would classify them as male of female.

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Reading it in a probability theory light, with some OO programming thrown in :

Child A=new Child("Chris", Gender.boy);
Child B=new Child("Chris", ??????????);
The problem is that
  • We don't know the gender of "Child B", nor its probabilities.
  • Querying by name alone is ambiguous.
So querying through some hypothetical "returnGenderForName("Chris")
function, depending on the implementation, it will either return the first "Known good" Chris (Child A, which is 100% a boy) with 50% chance (so that's 50% already for "Chris is a boy" or the other, pathological "Chris" with equal 50% chance, for which however we don't know the gender.

So the chances are really P(A)*P(A.Boy)+P(B)*P(B.Boy).

We suppose that P(A) and P(B) are equal and have a value of 1/2 (50%) since our "querying" might return either Child A or B. P(A.Boy) = 1 (or 100%), and P(B.Boy) is unknown.

TL;DR : Chances that "Chris" (ambiguously defined as above) is a boy can be anything between 50% and 100%. If both genders are equally probable, the the chance is 75%.

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They could be goats. It wouldn't matter.

I think I'm gonna copy off of Jodwin's paper. Don't tell on me.

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This is actually just another rehash of those "two sons/boys probability problem". Yawn.

From a mathematical standpoint, they are weakly-posed probability problems, because there are often implicit hidden assumptions and/or tricky wording, while those who propose them only clarify a posteriori to justify their proposed solution.

Sometimes this is just due to them being copied/passed on in a sort of "broken phone" kind of way, just like other similar problems are e.g. the Madmen with Blue Eyes Island or The Werewolf Village Epidemic recursive problems: almost inevitably they're worded ambiguously or leave out certain essential assumptions.

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If I had to guess (based on the original question alone) I'd say somewhere between 0% and 33%. Why would two siblings have the exact same first name (except when shortened)? I don't know of any other masculine full names (for which "Chris" is short) other than Christopher (off the top of my head), so it is highly probably that the other Chris (if indeed there are two) is short for Christine or some such feminine name.

On the other hand, there is a 100% probably that Chris is a boy, because it was already stated that he is.

On the third hand, what everyone else said..

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Having two kids named Chris makes sense if they have different mothers, in which case there's a very high probability they're both boys. Otherwise I agree with bytor.

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He doesn't state in wich capacity he got the two kids. For all we know he can have these two kids in his class, in his house, in his sniper scope. :p

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This more of an ill-poosed problem forcing you to work on vague assumptions. E.g. the name "Chris" makes you think that it MUST be a boy's name, but nowhere in the problem's context is this clearly stated.

As someone else pointed out, "two kids" could refer to two goats, and the "Chris" mentioned soon after could be a totally unrelated (human) kid, while the final mention of Chris is ambiguous.

So you have essentially have a question asked with no proper context. What a shitload of fuck.

There are better ways to phrase the problem, that's the only thing I'm 100% sure.

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Epyo said:

I have two kids named Chris. Chris is a boy. What is the probability that Chris is a boy?

If you're talking about the one who is a boy, then 100%. If you're talking about the other kid, 50%.

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GreyGhost said:
Having two kids named Chris makes sense if they have different mothers, in which case there's a very high probability they're both boys.

Also one mother. For example, one is called Christopher, the other Christian, and they both get called "Chris" at places (but probably not at home.)

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Using USA statistics, there's about 9 boys named Chris for 1 girl named Chris. Assuming all sentences are related and not a semantic riddle, there should be a 95% chance Chris is a boy.

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I'm sure someone is laughing all the way while typing in the results of this threads in some fucked-up psy-op research paper.

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myk said:

Also one mother. For example, one is called Christopher, the other Christian, and they both get called "Chris" at places (but probably not at home.)

That's a possibility. If in due course there's a third son I suppose he could be called Chrysalis.

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But according to the benevolent dictator of all knowledge, wiki answers, 0.033% to 0.05% of people are hermaphrodites. Now if the second kid was named Maes, that would be easy; 100% probability of being a girl. Anyway, so I don't have to do any work, I'm just going to choose 'girl', then if I'm wrong, force Chris to drink estrogen like the government did to Alan Turing. Plus Chris could be an ant. I'd tell you what percentage of the population is male vs. female in ants, but google was doing that thing where it only spits out articles you can't read and have to buy, on citeseerx probably to compete with bing (yeah right, to appear to compete with bing since they're in cahoots).

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boris said:

42

funny, I don't much care for the like feature on facebook, but I would like such a feature on the dw forums.

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Darnit. I keep thinking about this.

If you only take the info provided (one is a boy), the question posed (is Chris a boy?) could refer to either entity. The Chris whose gender is unknown could be either gender so there is a 50% chance that it is a boy (or girl). You can't factor-in any other ratios for the '50%' Chris to be either because no info is given to base it on. Since '50%' Chris is only half the equation, you have to subtract half of that from '100%' Chris.

75% and that's my final answer!

(Maes was sitting closer so I copied off of HIS paper)

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Assuming he meant to say that one Chris is a boy, and is asking the gender of the other Chris; also, assuming that he's crazy like George Foreman and has given the same name to multiple children; futhermore, assuming that both genders have an equal chance of being born:

Sort them in order of birth (even twins won't be born at exactly the same time), so the possibilities are:

  • boy, boy
  • boy, girl
  • girl, boy
  • girl, girl
The last one (two girls) can be ruled out since we know that at least one is a boy. So, there are three possibilities: Chris has a brother, also named Chris; Chris has a younger sister named Chris; Chris has an older sister named Chris. Therefore the probability that the other Chris is a boy is 1/3.

(The above is probably wrong, I almost failed stats...)

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Jodwin said:

Since we know that Chris A is a boy, but nothing about Chris B, it's safe to assume that Chris B is either a boy or a girl. Still, we do not know whether the second Chris mentioned in the question is the same as the first Chris. Thus:
If Chris A is a boy and Chris B is a girl, we have two cases: Chris 1 has to be Chris A, since he is the only boy, but Chris 2 may be either Chris A or Chris B. This would mean there's a 50 % chance so far that Chris 2 is a boy.

Alternatively, both Chrises might be boys. In this case, Chris 1 might be either Chris A or B and Chris 2 might be either Chris A or B. Which ones they are is irrelevant, but still, we have four more cases.

Thus, there are six different cases, only one where Chris 2 is not a boy. Therefor the probability of Chris 2 being a boy is 83.333%


Due to recent findings, I'm forced to re-visit my original theory. Since it has come to light that on average the human sex ratio of people born is 1.1 men for each woman, the numbers need checking. In particular, the case where Chris A is a boy and Chris B is a girl. The likelihood of Chris B being a girl is not 50 %, but 45 %.

So, since we know that Chris A, who is the same as Chris 1, is certainly boy, we can conclude that if Chris 2 is also Chris A the probability in this case is 100 %. However if Chris 2 happens to be Chris B, whose gender is girl, the probability of him being a boy is currently 0 %. This, and the four 100 % possibilities from the case where both Chrises are boys still stand.

However, what is different is that these possibilities need to be weighted to represent the sex ratio. The case where the two Chrises are of different gender gives Chris 2 a 50 % chance of being a boy. However, this situation itself has only 45 % chance of happening, whereas the other case of both Chrises being boys has the chance of 55 %.

Thus, the probability of Chris 2 being a boy is ( (100 % + 0 %) * 0.45 + (100 % + 100 % + 100 % + 100 %) * 0.55 ) / ( 100 % * 6 * 0.50 ) = 88.333 %.

CODOR said:

(The above is probably wrong, I almost failed stats...)

In statistics, everything depends on the assumptions you make and the results you want to gain. ;)

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Formulate this mathematically, and I'll think about it. Of course, there would be little need to, as it would be somewhat trivial.

Actually, Boris's answer is quite apposite, as the whole point of the answer "42" is that we don't know what the question is.

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The OP text could be written in an alien language with different intended meaning entirely, and just by sheer coincidence happens to make grammatical sense in english too.

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Jodwin said:

...the human sex ratio of people born is 1.1 men for each woman...

But that assumes that either one is human. They could be goats.

Look at it without making ANY assumptions.

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