Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: The Probability Myth vs the Sex of the Other Child
Replies: 37   Last Post: Feb 15, 1998 11:44 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Lee Lady

Posts: 24
Registered: 12/12/04
Re: The Probability Myth vs the Sex of the Other Child
Posted: Feb 8, 1998 1:33 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply



Note: This corrects a misprint in my previous article which makes *me*
look really stupid. I hope the previous version has been cancelled.

In article <6bka41$7mq@bgtnsc02.worldnet.att.net>,
Eldon Moritz <elmoritz@worldnet.att.net> wrote:
>> From: Alan Morgan <amorgan@CS.Stanford.EDU>
>> In article <6bd4p8$942@bgtnsc02.worldnet.att.net> Eldon Moritz writes:

>> >
>SNIP<
>> >"A lady has two children, at least one of which is a girl. What is the
>> >probability that she has two girls?"
>> >
>> >The answer is one-half, but the conventional argument seems to say it is
>> >one-third. Very obviously there is a flaw, an error in the conventional
>> >argument. Can you find it?

>>
>> Nope. There isn't one (unless you are putting some creative spin on
>> the problem that other people are not).

>
>Here we are opposed. I said there is a fallacy. You said flat out there is
>not. You think I am lying or real stupid or probably both.


It is very unlikely that you are lying. And you don't have to be stupid
to make the mistake you did. In fact, it's the same mistake almost
everyone makes when they first encounter this problem. And in fact, it's
not even clear that it is a mistake, since it's mostly a question of how
you interpret the problem.

It's very difficult to state this problem in a way that makes it obvious
what is given in the problem. The trouble is that most people don't
realize that there are two possible interpretations. Once you realize
that, I think most people would agree that the phrase "at least one"
should be interpreted in the way it is in probability courses. This
interpretation makes you wrong.

First possibility: You encounter a lady on the street. She has a little
girl with her who is her daughter. You ask her if she has any other
children and she has, "Yes, I have another child."

What is the probability that her second child is a girl? One-half, just
as you have claimed.

Second possibility: You are in the audience for a talk show. The host
asks all the women in the audience who have at least one daughter to
raise their hands. He chooses one of the women who have raised their
hands and asks, "How many children do you have?" She answers "Two."
What is the probability that both her children are girls? Answer: One
third, just as is claimed in probability classes.

Now I realize that for many people, it's still hard to see at first why
these two situations are different. So consider a third possibility:
Same audience, host asks all the women in the audience whose *youngest*
child is a girl to raise their hands. He chooses one and asks, "How many
children do you have?" and she answers "Two." What is the probability
that the other child is also a girl? Answer: One-half, just as you
claim.

(Fourth possibility: Instead of saying "youngest" he says "oldest." The
answer is still one-half.)

The third situation is essentially the same as the first possibility.
The question of whether you're really stupid or not can be settled by
seeing whether, after thinking about it, you can understand why this is
different from the second situation.

Can you see that in the third situation there will be fewer women with
their hands raised than in the second? Can you also notice that all the
women who have two daughters will have their hands raised both times
(assuming that all the women in the audience have exactly two children)?
Can you see why this means that the proportion (probability) is going to
be different in the two cases?

--
Trying to understand learning by studying schooling
is rather like trying to understand sexuality by studying bordellos.
-- Mary Catherine Bateson, Peripheral Visions
lady@Hawaii.Edu






Date Subject Author
2/5/98
Read The Probability Myth vs the Sex of the Other Child
Eldon Moritz
2/5/98
Read Re: The Probability Myth vs the Sex of the Other Child
Nat Silver
2/5/98
Read Re: The Probability Myth vs the Sex of the Other Child
Martin
2/5/98
Read Re: The Probability Myth vs the Sex of the Other Child
Chuck Cadman
2/5/98
Read Re: The Probability Myth vs the Sex of the Other Child
Jim P. Ferry
2/5/98
Read Re: The Probability Myth vs the Sex of the Other Child
Jeffery J. Leader
2/9/98
Read Re: The Probability Myth vs the Sex of the Other Child
Per Erik Manne
2/9/98
Read Re: The Probability Myth vs the Sex of the Other Child
standebj@SLU.EDU
2/5/98
Read Re: The Probability Myth vs the Sex of the Other Child
William L. Bahn
2/6/98
Read Re: The Probability Myth vs the Sex of the Other Child
Robert Hill
2/6/98
Read Parents! Look here! (was: The Probability Myth vs the Sex of the Other Child)
Erland Gadde
2/8/98
Read Re: Parents! Look here! (was: The Probability Myth vs the Sex of the Other Child)
Robert Israel
2/9/98
Read Re: Parents! Look here! (was: The Probability Myth vs the Sex of the Other Child)
Christian Bau
2/9/98
Read Re: Parents! Look here! (was: The Probability Myth vs the Sex of the Other Child)
David Kastrup
2/15/98
Read Re: Parents! Look here! (was: The Probability Myth vs the Sex of the Other Child)
Onno Garms
2/15/98
Read Re: Parents! Look here! (was: The Probability Myth vs the Sex of the Other Child)
Terry Moore
2/6/98
Read Re: Parents! Look here! (was: The Probability Myth vs the Sex of the Other Child)
Jon Haugsand
2/6/98
Read Re: The Probability Myth vs the Sex of the Other Child
Dennis Rakestraw
2/6/98
Read Re: The Probability Myth vs the Sex of the Other Child
Chuck Cadman
2/7/98
Read Re: The Probability Myth vs the Sex of the Other Child
Horst Kraemer
2/8/98
Read Re: The Probability Myth vs the Sex of the Other Child
Eldon Moritz
2/8/98
Read Re: The Probability Myth vs the Sex of the Other Child
Misha Kapushesky
2/8/98
Read Re: The Probability Myth vs the Sex of the Other Child
Lee Lady
2/9/98
Read Re: The Probability Myth vs the Sex of the Other Child
Horst Kraemer
2/8/98
Read Re: The Probability Myth vs the Sex of the Other Child
Adam Meikle
2/9/98
Read Re: The Probability Myth vs the Sex of the Other Child
Robert Hill
2/9/98
Read Re: The Probability Myth vs the Sex of the Other Child
standebj@SLU.EDU
2/9/98
Read Re: The Probability Myth vs the Sex of the Other Child
Robert Hill
2/9/98
Read Re: The Probability Myth vs the Sex of the Other Child
Nat Silver
2/9/98
Read Re: The Probability Myth vs the Sex of the Other Child
Jan Kristian Haugland
2/9/98
Read Re: The Probability Myth vs the Sex of the Other Child
Nat Silver
2/10/98
Read Re: The Probability Myth vs the Sex of the Other Child
Robert Hill
2/11/98
Read Re: The Probability Myth vs the Sex of the Other Child
Kjell Fredrik Rogstad Pettersen
2/11/98
Read Re: The Probability Myth vs the Sex of the Other Child
David Kastrup
2/11/98
Read Re: The Probability Myth vs the Sex of the Other Child
Dennis Rakestraw
2/10/98
Read Re: The Probability Myth vs the Sex of the Other Child
John Rickard
2/10/98
Read Re: The Probability Myth vs the Sex of the Other Child
n.lalu
2/13/98
Read Re: The Probability Myth vs the Sex of the Other Child
John Rickard

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.