Comments | combinator: MathBlog: Kid A and B (Every Boy In His Right Place)

combinator

MathBlog: Kid A and B (Every Boy In His Right Place)

Jun 09, 2005 22:29

I think this problem is worth thinking about even if you don't think of yourself as a math person (and especially in that case trying the penny flipping game). I first heard about it in the "Ask Marilyn" column ( Read more... )

Comments 8

r_transpose_p June 10 2005, 08:55:17 UTC

The sheer linguistict wankery involved here makes it sound like a mensa puzzle where the correct answer is #1.

Of course, I read it and pick number 2.

Had the question read "At least one of the two children is a boy" I would've come to a different conclusion.

leko June 10 2005, 12:15:31 UTC

Interesting. I think the fact that the first answer gives a sort of aside example, it seems like the more likely answer. Also, I think the fact that it's an easy and reasonable conclusion, and it comes before the convoluted conclusion, makes it more likely to be chosen ( ... )

dvarin June 10 2005, 14:52:19 UTC

In most contexts "one of them is a boy" implies that the other is not a boy, so the probability of them both being boys is 0. :P

dwindlehop June 10 2005, 18:43:01 UTC

My answer is that it depends on the selection process for families. If you were presented with a bunch of families with two children and eliminated the ones that had both girls, then wham! 1/3. If you are presented with a family and are told that they have at least one boy, then 1/2. Makes it analogous to the pennies.

zml June 10 2005, 18:56:16 UTC

#1 is the right answer. It's a funny brain teaser that I've seen a number of times at this point, and is also intimately related to the "Let's Make A Deal" problem.

combinator June 10 2005, 20:12:31 UTC

Background: You're at a game show. There are 3 doors. You know one door holds a prize. You pick a door. Then, a second door is revealed to you which does not contain a prize. You then have the option of switching doors - should you ( ... )

zml June 10 2005, 20:43:21 UTC

The difference you are citing is basically the difference between "that one is a boy" versus "one of them is a boy".

#1 is "She has two children and one of them is a boy."
#2 is "She has a boy named Alex and another child." (Similarly, if she walks in with her son, the probability is 1/2 that the other child is a boy.)

That's my reading, at least. If you say "one of them is a boy" after seeing the child, the statement is no longer sitting in a void. Yes, it's very much like quantum mechanics. :)

The relation to LMAD is that the solution to statement #1 (eliminating permutations) is how LMAD is solved, too (IIRC. Maybe I'm crazy, though. I probably shouldn't rederive that at work but, um, it's Friday afternoon.)