Re: The "two child problem"

["Stanley J. McCaslin" <mccaslin@pscosf.peru.edu>]

At 08:37 AM 7/28/97 -0800, you wrote:
> Marilyn had previously dealt with the following problem:  A man and a 
> woman each have two children.  The man's older child is a son and at 
> least one of the woman's children is a son.  Is either more likely 
> than the other to have two sons?
>
> OK, I'll bite.  There are four possible combinations of two children

Older    Younger
Son      Son
Son      Daughter
Daughter Son
Daughter Daughter

(Assume each is equally likely)

If you know that the man's older child is a son, you narrow your 
choices down to two, one of which is son son, so there is a one out
of two chance that the man has two sons.  If you know only that the
woman has a son, you narrow your choices to three, so there is now
a one out of three chance that the woman has two sons.  Thus, with the
knowledge at hand, the man is more likely to have two sons.