Let's Hear It For The Boys

May 16, 1998

RAY: Here it is. If a mother has two kids and the older one is a boy. What are the chances the younger is a boy? OK.

TOM: Whoa.

RAY: Well, that's only half the puzzler.

TOM: I know this puzzler. This is a killer.

RAY: And the answer is 50-50. OK. You got that?

TOM: Yeah.

RAY: So, I'll give you that part.

TOM: Yeah. So, she's got a boy kid

RAY: Who's the older?

TOM: Right.

RAY: The mother has two kids. The older one is a boy, what are the chances the younger one is a boy?

TOM: Fifty-fifty.

RAY: Got it?

TOM: I'm with you on that.

RAY: You paying attention now?

TOM: Yeah.

RAY: Now, suppose that same mother. No. Suppose a different mother has two kids and one of them is a boy, what are the chances --

TOM: That the other one --

RAY: That the other one is a boy? Well, it's got to be 50-50. Right?

TOM: You would think.

RAY: Wrong.

TOM: Of course.

RAY: So, what are those chances? Now, if you're thinking --

TOM: And why? We want all the calculations, man.

RAY: I got them all right here, man. Cause Steve didn't send the answer, but, of course --

TOM: We don't need answers.

RAY: We don't need no... Oh yeah, we do need, just send the puzzler. Send the stinkin' answer.

TOM: Yeah. This is very good. Very good.


RAY: Now if you draw little pictures... there are four possible scenarios.

TOM: Yeah.

RAY: Older boy, younger boy. We'll call that B and B. Older boy, younger girl. Older girl, younger boy.

TOM: Um hmm. Yeah.

RAY: And older girl, younger girl. That's it. If you're going to have two kids, that's it. All right? Now, in the first case --

TOM: Of course.

RAY: If I say... When I say the older one is a boy --

TOM: Um hmm.

RAY: That it immediately leaves out the last two --

TOM: Exactly.

RAY: Possibilities.

TOM: That's right.

RAY: OK? It can only be boy-boy or boy-girl.

TOM: That's right.

RAY: Right. So, in order for it for the other one to be a boy, it's a 50-50 chance.

TOM: Right. You can have boy-boy, boy-girl.

RAY: Right. Or, now... Now!

TOM: Yeah.

RAY: When I say that one of them is a boy, I believe... Believe it or not it is this counterintuitive --

TOM: It certainly is.

RAY: It becomes harder for the other one to become a boy.

TOM: Um hmm.

RAY: And the chances are one in three cause if you look at the scenarios, you have boy-boy, boy-girl and girl-boy.

TOM: Sure.

RAY: Right? For the other one to be a boy, it's gotta be choice #1 which is boy-boy cause you already said that one of them is a boy, how can the other one be a boy? There's one chance in three. Hard to believe. Isn't it?

TOM: It's hard to believe.

RAY: I don't believe it.

TOM: I don't either.

RAY: Well, it's --

TOM: But it is true.

RAY: It is true.

TOM: And evidently, evidently Marilyn has a lot of data and the way she... I remember this puzzler now. You said you stole it from Marilyn.

RAY: Well, I didn't really steal it from Marilyn, I stole it from Steven Miller.

TOM: Yeah, but don't forget, Marilyn stole it from somebody else so, it's fair game. But the way that she proved it, she said here's how I'm going to prove it and she asked people to send her letters --

RAY: Oh yeah.

TOM: Anyone who had two kids and the first one was a boy, how many had a second one a boy and two kids who, one of whom was a boy, how many had second one as a boy --

RAY: Right, and --

TOM: And it came out --

RAY: She proved it empirically --

TOM: Empirically.

RAY: Just like we did with the Monty Hall thing.

TOM: Exactly, which I guess is OK, but I like the more elegant, abstract mathematical solutions, myself. I mean, but that's the kind of guy I am, I'm an abstract kind of guy.

RAY: You're abstract all right. Do we have a winner this week?

TOM: I don't remember. Uh. Ha! Yes, we do. The winner is David Ward from Atlanta, Georgia.

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