🚀 go-pugleaf

In article <6670016@hplsla.hp.com> barryg@hplsla.hp.com (Barry Gunn) writes:
>>>You meet the daughter of a friend of yours on the street.  You know that your
>>>friend has two children.  You think to yourself, "Ignoring the occurrence of
>>>twins, and sex-linked differences in birth rates and infant mortality, what
>>are
>>>the odds of this girl's sibling also being a girl?"
>>>-----------------+-------------------------------
>>Two child families are uniformly distributed between MM,MF,FF,FM, in birth
>>order.  Again, all four possibilities are equally likely.  Stop here.  Make
>>sure you believe that.
>>
>>Now, since at least one is F, the MM drops out, leaving MF, FF, FM, so that
>>there is only a one third chance that the sibling is a girl.
>
>But you meet the F on the street. So MF and FM are the same in this case
>(but not the way the problem is usually stated). I say 50%.

I disagree. I made this mistake once myself and promptly realized the flaw.
Why don't you consider this metaphor : you have these teeming
billions of sibling-pairs in the Earth (yeah, I mean all continents,
islands, places hitherto undiscovered or unknown, etc. etc. taken
together ad nauseam :-) ) ?  Now, it's quite easily seen that FF 
pairs comprise only 25 % of _this_ population (assuming that the
birth events of a pair of siblings are independent, thereby precluding 
identical twins, etc.). 50 % of this population will comprise MF
sibling pairs, and the remaining 25 %, MM pairs.

Now, you the witness of one of a pair of siblings, are a Martian
and have just floated down on the earth from Mars on a spaceship,
on a special invitation from Presidents Clinton and Yeltsin,
and see one female member of a pair of siblings, who has been sent
by her Dad to receive you.  You have had numerous inter-planetary 
conversations with her Dad (mostly on new and exciting ways of
proving that P equals NP :-) ), and know that he has two children, 
but you've never asked him their sexes. Now without any other info, 
it's a fair assumption that you'll encounter sibling pairs on the Earth
in proportion to their relative frequencies of occurrence.  Hence, 
the female sibling you encounter is twice as likely to be a part of a
mixed sex pair than of an FF pair.  Hence, the other sibling being a
female has probability 1/3.

Hope it helps.

Kanad