🚀 go-pugleaf

In article <1993Jan26.155709.25082@cs.cornell.edu>, karr@cs.cornell.edu
(David Karr) wrote:
> 
> In article <C1GuHw.zuF@austin.ibm.com> bmoore@sunfish.austin.ibm.com (Bryan Moore) writes:
> >[...]
> >Back to the dice... Roll two dice 100 times. Get 100 pieces of paper and
> >write the results of the first die on one side and write the results
> >of the second die on the other side of the piece of paper. Put all the
> >pieces of paper in a hat. Now pick a piece of paper out of the hat.
> >You see a six on the piece of paper, what is the probability that the
> >other side has a six? IT IS 1/11!!!!!!! 
> 
> No, it's 1/6.  Have you tried it?  Get someone who really understands
> probability to explain it to you.  Or you can simulate it easily on a
> computer, but remember, a paper with two 6's can be selected in two
> different ways but a paper with only one 6 can be selected in only one
> way (if the first side you look at is the other side you have to
> discard the event).
> 
> -- David Karr (karr@cs.cornell.edu)


Well, you're right, but when you ask the problem the CORRECT way, that
is, don't mention meeting someone on the street, then the answer is
1/3, not 1/2.  If there were a club for every family in the US that
had two children at least one of which was a girl, and everyone
qualified joined, then only 1/3 of the member families would have the
other daughter also a girl.

Or, in terms of the paper hat, you have to look at both sides.  If EITHER
side is a six, then the probability that the OTHER side is a six is
1/11.  It's the unintuitiveness of the way you're given the information
that obscures the answer.

Bob Hearn
Spartacus Software

Opinions expressed here are those of my empolyer, since that's me.