From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Thu May 30 2002 - 12:51:27 MDT
Harvey Newstrom wrote:
>
> On Thursday, May 30, 2002, at 11:13 am, spike66 wrote:
>
> > Harvey Newstrom wrote:
> >
> >>> You collect two kinds of mushrooms, the
> >>> fleebs and the kloongs. 10% of the fleebs will give you
> >>> diarrhea, whereas 20% of the kloongs will. You know that
> >>> most will not harm you at all, but you know that devouring
> >>> a kloong is twice as dangerous as eating a fleeb.
> >>
> >> In your above example, picking the "good" mushrooms will statistically
> >> make you sick every tenth mushroom. If you eat 10 mushrooms in a
> >> meal, you still get sick 100% of the time.
> >
> > Well, 63%. But lets not get all mathematical. {8^D
>
> If you reject all the kloongs and only pick fleebs, then your 10
> mushrooms per meal are all fleebs. If every tenth fleeb is bad, on
> average you will get one bad fleeb every meal. Every single meal will
> make you sick.
Each fleeb has a 0.9 chance of being good. Ten fleebs have a 0.9**10 =
0.348 chance of being good. Ergo, a meal of ten fleebs has a 65% (why 63%,
Spike?) chance of making you sick. No more, no less.
It is not true that if every tenth fleeb is bad, you get one bad fleeb per
meal of ten fleebs. The bad fleebs are not evenly spaced; hence, some meals
of ten fleebs will contain two or more bad fleebs. The converse of this is
that some meals of ten fleebs will contain zero bad fleebs.
-- -- -- -- --
Eliezer S. Yudkowsky http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence
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