An assembly is faulty with probability p. A test correctly identifies a faulty or nonfaulty assembly with probability q. What is the probability that the test declares an assembly faulty?
Partition by the true condition. A faulty assembly is declared faulty with probability pq. A nonfaulty assembly is incorrectly declared faulty with probability (1−p)(1−q). These disjoint events sum to pq+(1−p)(1−q), A.
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