**From:** John Stick (*johnstick@worldnet.att.net*)

**Date:** Sat Mar 29 2003 - 20:46:57 MST

**Next message:**Psy-Kosh: "Re: Bayesian story problem SPOILER WARNING: attempt at solution"**Previous message:**Psy-Kosh: "Re: Bayesian story problem SPOILER WARNING: attempt at solution"**In reply to:**Psy-Kosh: "Re: Bayesian story problem SPOILER WARNING: attempt at solution"**Next in thread:**Psy-Kosh: "Re: Bayesian story problem SPOILER WARNING: attempt at solution"**Reply:**Psy-Kosh: "Re: Bayesian story problem SPOILER WARNING: attempt at solution"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Psy-kosh,

You had it right up to the last calculation: try reducing that fraction

again.

Psy-Kosh wrote:

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*>
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*>>A couple of #SL4ers have asked me for this, so I'm posting it to
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*>>SL4-the-mailing-list:
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*>>
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*>>Suppose you have a large barrel containing a number of plastic
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*>>
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*>>
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*>eggs. Some
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*>
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*>
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*>>eggs contain pearls, the rest contain nothing. Some eggs are
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*>>
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*>>
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*>painted
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*>
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*>
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*>>blue, the rest are painted red. Suppose that 40% of the eggs are
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*>>
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*>>
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*>painted
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*>
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*>
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*>>blue, 5/13 of the eggs containing pearls are painted blue, and 20%
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*>>
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*>>
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*>of the
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*>
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*>
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*>>eggs are both empty and painted red. What is the probability that
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*>>
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*>>
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*>an egg
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*>
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*>
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*>>painted blue contains a pearl?
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*>>
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*>>As a check on your calculations, the likelihood that a red egg is
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*>>
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*>>
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*>empty,
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*>
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*>
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*>>divided by the likelihood that an egg contains a pearl, equals
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*>>approximately .51. To use this information in the problem, of
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*>>
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*>>
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*>course,
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*>
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*>
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*>>would be cheating.
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*>>
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*>>
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*>>
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*>
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*>Spoiler space:
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*>
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>.
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*>
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*>
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*>Given:
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*>
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*>P(B)=2/5
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*>
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*>P(B|P)=5/13
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*>
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*>P(~B,~P)=1/5
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*>
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*>We have
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*>
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*>1-P(B)=P(~B)=3/5
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*>
*

*>We can subtract the third item from the fourth to get the probability
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*>that an egg contains a pearl and is red:
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*>
*

*>P(~B)-P(~B,~P)=P(~B,P)=2/5
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*>
*

*>Also we have the probability that an egg containing a pearl is red:
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*>
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*>1-P(B|P)=P(~B|P)=8/13
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*>
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*>Now, we are able to determine the total probability that an egg
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*>contains a pearl:
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*>
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*>P(~B|P)P(P)=P(~B,P) so P(P)=P(~B,P)/P(~B|P)=(2/5)/(8/13)
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*>
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*>P(P)=13/20
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*>
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*>So.... (Hail Bayes! All Hail Rationality! :)
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*>
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*>P(P|B)=P(B|P)P(P)/P(B)
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*>
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*>P(P|B)=(5/13)*(13/20)/(2/5)=1/10=10%
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*>
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*>=DC4o
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*>
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*>
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**Next message:**Psy-Kosh: "Re: Bayesian story problem SPOILER WARNING: attempt at solution"**Previous message:**Psy-Kosh: "Re: Bayesian story problem SPOILER WARNING: attempt at solution"**In reply to:**Psy-Kosh: "Re: Bayesian story problem SPOILER WARNING: attempt at solution"**Next in thread:**Psy-Kosh: "Re: Bayesian story problem SPOILER WARNING: attempt at solution"**Reply:**Psy-Kosh: "Re: Bayesian story problem SPOILER WARNING: attempt at solution"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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