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Topic: probability question
Replies: 9   Last Post: Mar 13, 2008 4:08 PM

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 The World Wide Wade Posts: 1,507 Registered: 2/24/07
Re: probability question
Posted: Mar 13, 2008 4:08 PM

In article
Ray Vickson <RGVickson@shaw.ca> wrote:

> On Mar 11, 6:56 pm, Steven <sgottlie...@hotmail.com> wrote:
> > Suppose you meet me on a street corner and I introduce you to my son who is
> > with me. I inform you that I have another child at home. What is the
> > probability that my other child is a girl.
> > I looked at the sample space which I claim is bb, bg, gb and so the answer
> > is 2/3. Is this correct?
> > Steven

>
> Yes, provided that you don't say which child is older. If you do say
> which is older, the probability becomes 1/2! You can also look at the
> problem this way: you toss a coin twice and announce that you got at
> least one Head. What is the probability the other outcome was a Tail?

"Other" is not well-defined in this coin experiment, but it is in the
OP's problem. I think your coin example models the following: You meet
me on the corner, I tell you I have two kids at home, you ask if
they're both girls, and I say no. Then the probability is 2/3 that I
have a daughter. But if I'm out with one of my two kids, who's a boy,
then the probability my other kid is a girl is 1/2 - assuming I'm
equally likely to have my other kid with me. I think this is a better
model for the OP's problem. The coin problem analogous to this is: I
have two coins, I toss each, then randomly choose the result of one of
the tosses to announce. If I say heads, what is the probability the
other toss is tails?

> Again, the probability that the other outcome is a Tail is 2/3 if you
> don't say whether your announced Head was first or second, and is 1/2
> if you do announce its position.
>
> R.G. Vickson

Date Subject Author
3/11/08 Steven
3/11/08 Dan Heyman
3/11/08 Bob Delaney
3/12/08 RGVickson@shaw.ca