Date: Sat, 24 Apr 1999 22:00:26 -0700
From: Dan <dgray@justin-siena.napanet.net>
To: Pinhole Listserv <pinhole@exploratorium.edu>
Subject: Re: pinhole probability
> >
> >1) girl girl
> >2) girl boy
> >3) boy girl
> >4) boy boy
> >
> >Assuming that
> >A) these are equally likely ( Prob = 1/4 each)
> >and
> >B) If you meet a girl it is equally likely that she is in category 1) 2) or 3)
> >
> >then the odds brother:sister = 2:1
> >
> >
> >If you meet a girl who is first born, the answer is 1:1
> >The surprise comes because the 4 categories are labelled by both sex (2
> >possibilities) and order of birth (2 possibilities). 2x2 = 4 categories
> >
> >This is a good problem because its solution utilizes the general approach
> >of enumerating all possibilities and then seeing which of them satisfy the
> >criteria or conditions of the posed question. The Monte Hall problem works
> >the same way.
> >
> >... Thomas
> >
But wait, isn't it twice as likely she would be from group A since there are two
slots there for sisters, older or younger? If I take the 8 people listed above and
remove the boys, I have 4 girls to interview. Two of them are from group A, one
each from B and C. That takes the odds back to 1:1.