At a plant, 20% of all the produced parts are subject to a special electronic inspection. it is known that any produced part which was inspected electronically has no defects with probability 0.95. for a part that was not inspected electronically this probability is only 0.7. a customer receives a part and find defects in it. what is the probability that this part went through an electronic inspection?

Question

Mylie Burnett

Mathematics

6 October, 03:03

At a plant, 20% of all the produced parts are subject to a special electronic inspection. it is known that any produced part which was inspected electronically has no defects with probability 0.95. for a part that was not inspected electronically this probability is only 0.7. a customer receives a part and find defects in it. what is the probability that this part went through an electronic inspection?

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Timmy · Answer 1

solution:

P (inspect) = 0.20, P (no inspect) = 0.80

P (defect|inspect) = 0.05

P (defect|no inspect) = 0.30

P (defect) = P (defect|inspect) / timesP (inspect) + P (defect|no inspect) / timesP (no inspect) = 0.05/times0.20 + 0.30/times0.80 = 0.10+0.24 = 0.34

/frac{P (inspect and defect) }{P (defect) }

= 0.10/0.34 = 0.294