Conditional Probabilityhard
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Two machines, Alpha and Beta, produce microchips. Alpha produces 60% of output with a 2% failure rate, while Beta produces 40% with a 5% failure rate. A quality control system correctly identifies 95% of defective chips but incorrectly flags 3% of functional chips as defective. If a chip is flagged by the system, what is the probability it was produced by Alpha?
Two machines, Alpha and Beta, produce microchips. Alpha produces 60% of output with a 2% failure rate, while Beta produces 40% with a 5% failure rate. A quality control system correctly identifies 95% of defective chips but incorrectly flags 3% of functional chips as defective. If a chip is flagged by the system, what is the probability it was produced by Alpha?