Question

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?

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