198.Which Urn Gave the Ten
★★★conditional probabilityJane Street
Two identical-looking urns each hold ten chips. The first contains seven chips and three chips; the second contains nine chips and one chip. You pick an urn at random and draw a chip, and it is a chip. What is the probability that it came from the first urn?
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Both urns were equally likely beforehand, so compare only how readily each could have produced a ten.
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