From: Lee Daniel Crocker (lee@piclab.com)
Date: Tue Mar 25 2003 - 11:04:46 MST
> (spike66 <spike66@attbi.com>):
> I get 5/8 or about 62.5%, but I used classic
> methods not Baysian. Is that the right answer?
> It doesn't agree with your check. {8-| spike
I'm with Spike; I got 5/8 and didn't do anything Bayesian.
Let N = total eggs, Eb = empty blue eggs, Pb = blue eggs with
pearls, Er = empty red eggs, Pr = red eggs with pearls. Given
directly by the problem are:
N = Eb + Pb + Er + Pr (There aren't any green eggs, etc.) *
2/5 N = Eb + Pb (40% of the eggs are blue)
5/13 (Pb + Pr) = Pb (5/13 of eggs with pearls are blue)
1/5 N = Er (20% of eggs are empty and red)
Following from those, we get:
N = (2/5 N) + (1/5 N) + Pr
2/5 N = Pr (So 40% are red/pearl, 60% total red)
And then...
5/13 (Pb + 2/5 N) = Pb
Pb = 1/4 N
Since 25% of the eggs are blue with pearls, and 40% are blue,
then 5/8 of the blue eggs have pearls
* Now, maybe that first equation you didn't really mean to
specify, and that would indeed change the problem, but I suspect
it would become insoluble in that case.
-- Lee Daniel Crocker <lee@piclab.com> <http://www.piclab.com/lee/> "All inventions or works of authorship original to me, herein and past, are placed irrevocably in the public domain, and may be used or modified for any purpose, without permission, attribution, or notification."--LDC
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