Problem #83 MEDIUM
The Circuit Board Test
Amazon Apple Probability Optimization
Problem Statement
A factory produces circuit boards in batches of 100. Each batch is either entirely good (all 100 boards work) or entirely defective (all 100 boards fail). Before shipping, a quality controller tests individual boards from the batch. Each test costs 1 unit. If the batch is good, every board passes. If the batch is defective, each board fails its test independently with probability 0.9 (and passes with probability 0.1 — defective boards sometimes appear fine). The prior probability that any given batch is defective is 0.2. How many boards should the controller test to minimise total expected cost (testing cost plus cost of shipping a defective batch, where shipping a defective batch costs 500 units)?
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