= A batch consisting of 100 chips is produced by a manufacturing plant. If the manufacturing...

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= A batch consisting of 100 chips is produced by a manufacturing plant. If the manufacturing process is functioning properly, chips are only occasionally defective with each chip being defective with a probability of pgood 0.01. If the manufacturing process is faulty, chips are more often defective with probability Pfaulty = 0.25. The manufacturing history is such that the process is faulty 10% of the time. Quality control will test the manufacturing process by evaluating 3 chips from the batch. If they all test good, the process will be declared to be functioning properly, otherwise, if any of the tested chips are defective, the process is declared to be faulty. (a) What is the probability that the manufacturing process was faulty, given all chips tested were good)? (b) What is the probability that the manufacturing process was good, given at least one of the chips tested was defective? (c) What is the probability that the manufacturing process was good, given exactly one of the chips tested was defective? = A batch consisting of 100 chips is produced by a manufacturing plant. If the manufacturing process is functioning properly, chips are only occasionally defective with each chip being defective with a probability of pgood 0.01. If the manufacturing process is faulty, chips are more often defective with probability Pfaulty = 0.25. The manufacturing history is such that the process is faulty 10% of the time. Quality control will test the manufacturing process by evaluating 3 chips from the batch. If they all test good, the process will be declared to be functioning properly, otherwise, if any of the tested chips are defective, the process is declared to be faulty. (a) What is the probability that the manufacturing process was faulty, given all chips tested were good)? (b) What is the probability that the manufacturing process was good, given at least one of the chips tested was defective? (c) What is the probability that the manufacturing process was good, given exactly one of the chips tested was defective?