Riddle - Family with 2 Kids

Tim Folkerts · Nov 14, 2006

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?

Tim F

SteelMaiden · Nov 15, 2006

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)

Jim Wynne · Nov 15, 2006

SteelMaiden said:
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.

Craig H. · Nov 15, 2006

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

Jim Wynne · Nov 15, 2006

Craig H. said:
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'sthe Cove thread that deals with the Let's Make a Deal question, for those who don't know what we're referring to.

Tim Folkerts · Nov 15, 2006

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

Craig H. · Nov 15, 2006

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

.

Right?

SteelMaiden · Nov 15, 2006

Craig H. said:
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 .

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?

Craig H. · Nov 15, 2006

SteelMaiden said:
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?

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.

Tim Folkerts · Nov 15, 2006

Craig H. said:
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.

Tim F

Riddle - Family with 2 Kids

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