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An engineering project involves reinforcing a concrete beam. From previous experience it is thought that the probability of corrosion is 1%. A diagnostic test is performed on the reinforced beam. If corrosion is present, then the probability that the test will reveal it is 80% while the probability that the test will miss it is 20%. The diagnostic never yields false positives-that is, it will never indicate corrosion if corrosion is not present. What is the probability of discovering corrosion?
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