🚀 go-pugleaf

In article <1993Jan26.204422.15093@zip.eecs.umich.edu> kanad@quip.eecs.umich.edu (Kanad Chakraborty) writes:

[Original problem deleted]

>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.

[Metaphor deleted]

>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.

	Nobody seems to have noticed my original argument for 1/2, so I'll
respond to this one. Contrary to the author's intention, this is actually
a good way to see that the answer is 1/2. The key, once again, is that
there are two females in an FF pair and only one in a MF or FM pair.
Taking a cue from his argument, assume that there are 1000 sibling pairs
in the world. Of these pairs, 250 are MM, 250 are MF, 250 are FM, and 250
are FF. Now you see a female, so you know that she can't be part of an
MM. This limits you to the other 750 pairs. While it is true that there
are 500 mixed pairs remaining and 250 FF pairs remaining, there are 2 females
in each FF pair. Therefore, of the 1000 females in the mixed pairs and FF
pairs, 500 are in mixed pairs and 500 are in FF pairs. There is a 50%
chance the female you're looking at is from an FF pair, and hence her
sibling is female.
				-Ted Quinn
				 quinn@relgyro.stanford.edu