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Unformatted text preview: 0% of the eggs in the bin contain pearls, and 60% contain nothing. 30% of eggs containing
pearls are painted blue, and 10% of eggs containing nothing are painted blue. What is the probability
that a blue egg contains a pearl?
What do we know?  P (pearl) = 0.4, P (blue  pearl) = 0.3, and P (blue  no pearl) = 0.1.
We want to ﬁnd P (pearl  blue) 1 This is an application of Bayes theorem:
P (pearl  blue) =
=
= P (pearl ∩ blue)
=
P (blue)
P (blue  pearl)P (pearl)
=
P (blue  pearl)P (pearl) + P (blue  no pearl)P (no pearl)
0.3 · 0.4
0.12
=
= 2/3
0.3 · 0.4 + 0.1 · 0.6
0.12 + 0.06 (b) 1% of wo...
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 Spring '08
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