Blue oysters

You’re col­lect­ing ex­otic oys­ters in Nan­tucket, and there are two differ­ent bays you could har­vest oys­ters from. In both bays, 11% of the oys­ters con­tain valuable pearls and 89% are empty. In the first bay, 4% of the pearl-con­tain­ing oys­ters are blue, and 8% of the non-pearl-con­tain­ing oys­ters are blue. In the sec­ond bay, 13% of the pearl-con­tain­ing oys­ters are blue, and 26% of the non-pearl-con­tain­ing oys­ters are blue. You cre­ated a spe­cial de­vice that helps you find blue oys­ters. Would you rather har­vest blue oys­ters from the first bay or the sec­ond bay?

You’re en­couraged to try to solve this prob­lem your­self, and to re­frain from look­ing at the an­swer. The an­swer can be found in Bayes’ rule: Log-odds form.

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