I haven't seen this riddle here (at least I don't remember it, so it must have been a while if it was here).

A new family moves into a house on your block. You have been told that they have two kids, but you don't know the genders. You happen to see one of the kids, and it is a boy. What are the odds that the other is also a boy?

The obvious answer is 1:1, but is it correct? :confused: :yes: :nope:


Tim F

You know, the only thing I can think of here is that the "kids" are baby goats. but that still doesn't answer whether the 2nd will be male or female. For children, I think the national average says that 51.5% of the babies born to couples are boys. (49.something% born to single mothers are boys)

You know, the only thing I can think of here is that the "kids" are baby goats. but that still doesn't answer whether the 2nd will be male or female. For children, I think the national average says that 51.5% of the babies born to couples are boys. (49.something% born to single mothers are boys)

I know the answer to this one, so I won't spoil it, but I will say that it's not a trick question (no goats involved). Think sample space.

Is the reasoning to this answer the same as the "Let's Make a Deal" riddle?

Is the reasoning to this answer the same as the "Let's Make a Deal" riddle?

Insofar as it involves the contents of the sample space, yes. Here's (http://elsmar.com/Forums/showthread.php?t=15328)the Cove thread that deals with the Let's Make a Deal question, for those who don't know what we're referring to.

I will also say that the answer depends subtly on how the problem is posed and interpretted. :caution:

Even if you have heard the riddle before, the answer may be different than you think depending on just how the information is presented. :mg:


Tim

OK, here's a shot, or rather an answer to be shot at.

At first, we know there are 2 kids, (x=male, y=female). So, here are the possibilities:

xx
xy
yx
yy

Then we find out that one is x. so

xx possible
xy possible
yx possible
yy nope.

so, there is a 2/3 chance that the family has 1 boy (x) and 1 girl (y).

Right?

OK, here's a shot, or rather an answer to be shot at.

At first, we know there are 2 kids, (x=male, y=female). So, here are the possibilities:

xx
xy
yx
yy

Then we find out that one is x. so

xx possible
xy possible
yx possible
yy nope.

so, there is a 2/3 chance that the family has 1 boy (x) and 1 girl (y).

Right?
Actually, there is only two possibilities, xx or xy, you cannot have a yy (or a yx, if the first gene comes from the mother) gene combination, remember biology and s- education classes?:notme:

Since each new baby starts the genetic wheel of chance all over again, there will always be a 50/50 chance (or slightly higher according to statistics) that the second child will be a boy. no?

Actually, there is only two possibilities, xx or xy, you cannot have a yy (or a yx, if the first gene comes from the mother) gene combination, remember biology and s- education classes?:notme:

Since each new baby starts the genetic wheel of chance all over again, there will always be a 50/50 chance (or slightly higher according to statistics) that the second child will be a boy. no?

I just knew someone would see the xy thing biologically!

Anyway, the flaw I thought I might see in my logic involves the xy and yx. Can we eliminate the yx, because we found out the first one is a boy (x)? I don't think so, my (il)logic being that we don't know the birth order.

But, if we do eliminate the yx, we are back to 50/50.

I just knew someone would see the xy thing biologically!

Anyway, the flaw I thought I might see in my logic involves the xy and yx. Can we eliminate the yx, because we found out the first one is a boy (x)? I don't think so, my (il)logic being that we don't know the birth order.

But, if we do eliminate the yx, we are back to 50/50.

It looks like Craig is getting to the heart of the issue - the choices seem to be 1:1 odds or 1:2 odds. Is there a way to clearly show that one answer is corect? Are there ways to rephase the question to make the other answer correct?

I'll let you all grapple with this before I give my opinion. Which of course is the correct opinion.:rolleyes::lol:

Tim F

I haven't seen this riddle here (at least I don't remember it, so it must have been a while if it was here).

A new family moves into a house on your block. You have been told that they have two kids, but you don't know the genders. You happen to see one of the kids, and it is a boy. What are the odds that the other is also a boy?

The obvious answer is 1:1, but is it correct? :confused: :yes: :nope:

Tim F


The two children's sexes are independent of each other - assuming they aren't twins - (I think there is some sex-sex correlation in twins.) I think the confusion comes from the riddle using the words... 'the other is ALSO". The odds are approximately 1:1 (unless you're in China or some other place where girl kids are sometimes killed.) I believe this is analogous to the coin flipping - the next flip still has the same probability.

The sex of the first child has no bearing on the second. The question is "what is the sex of the second child". This would be (roughly) 50%, regardless of how many children are in the sample (family).

If the question was "what is the probability that a family will have two boys", it would be 25% as your possibilities are XX, XY, YX or YY as shown above. Or .5 X .5 = .25

If the question was "what is the probability that a family with one boy will have a second boy", the answer would be back to 50%. Options are only XX or XY, or mathmatically 1.0 X .5 = .5.

For the sake of simplicity, let us assume that the boy:girl birth rate is 50:50 (close enough). As Jim said, think sample space. There are three possible combinations (4 permutations as Craig H. pointed out but I don't think they matter).

Boy-Girl
Boy-Boy
Girl-Girl

Obviously, girl-girl is out. So we're left with:

Boy-Girl
Boy-Boy

I'm having a hard time getting my head around this one. Either you've spotted the Boy in column one and your chance that his sibling is a Boy the 50:50 shot in column two OR you've spotted one Boy in the matrix of 4 and chance that his sibling is a boy is 2 out of 3. Or maybe we do need to consider the possible permutations:

Boy-Girl
Girl-Boy
Boy-Boy
Girl-Girl

Strike Girl-Girl, the Boy is one of 6 in the matrix and the other Boy is a 3 of 5 shot OR the Boy is from column one and....
Is there a "Tim, you're giving me a headache" choice?

Is there a "Tim, you're giving me a headache" choice?So I cheated, Google to the rescue:
WARNING: SPOILER
Fuzzy Math: Reproductive Roulette (http://www.discover.com/issues/aug-06/rd/reproroulette/)

The New Jersey answer is:

nonnayerbusiness.

The New Jersey answer is:

nonnayerbusiness.

It's been a while since I've been to the Garden State, but I seem to remember something between "nonnayer" and "business." :notme:

So I cheated, Google to the rescue:
WARNING: SPOILER
Fuzzy Math: Reproductive Roulette (http://www.discover.com/issues/aug-06/rd/reproroulette/)

I swear I didn't google this before I posted my response. Surprised how close I was.

Unless, of course, there is a language twist to the wording that I have missed(?)...

Someone please send this to "Ask Marilyn" in the Sunday Parade column!!!

So I cheated, Google to the rescue:
WARNING: SPOILER
Fuzzy Math: Reproductive Roulette (http://www.discover.com/issues/aug-06/rd/reproroulette/)

Ah, but the statement of the problem is different on this page. They say:
"If a father of two tells you one of his children is a boy, what are the odds that the other child is also a boy?"

In my case, the parent didn't tell tell you one of the children was a boy, but rather you observed one child who was a boy. Even though it may sound almost the same - being told that one of the children is a boy vs observing that one of the children is a boy - I contend it makes a difference! In one case, the odds are 1:2 of the other being a boy, while in the other scenario, the odds are 1:1 of the other child being a boy!


I'll wait a bit before giving more details about why I believe the two are different. Let you cuss and discuss on your own to see if you agree with me. :frust: ;)



Tim

Here's my cuss:

http://elsmar.com/Forums/showpost.php?p=128269&postcount=3:mad: