30 of eggs containing pearls are painted blue and 10

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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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