A quality control inspector is inspecting newly produced items for faults. The i
ID: 3041547 • Letter: A
Question
A quality control inspector is inspecting newly produced items for faults. The inspector searches an item for faults in a series of two independent tests. If a flaw is actually present, there is 5% chance that it will not be detected in one test. If there is no flaw, the item will surely pass the test.
(a) [2 points] Assuming that an item has a flaw, what is the probability that it will be detected in the inspection (consisting of a series of two independent tests)?
(b) [6 points] Suppose 10% of all items contain a flaw, i.e., P(randomly chosen item is flawed)=0.1. What is the probability that a randomly chosen item will pass the inspection?
(c) [6 points] Given that an item has passed the inspection (i.e., no flaw detected in a series of two independent tests), what is the probability that it actually does not have any flaw?
Explanation / Answer
a) probability that it will be detected in the inspection given flaw =1-P(passess both the inspection test)
=1-(0.05*0.05) =1-0.0025 =0.9975
b)
P(randomly chosen item will pass the inspection) =P(not flawed and clear inspection+flawed and clear inspection)
=(1-0.1)*1+0.1*(1-0.9975)=0.90025
c) probability that it actually does not have any flaw given passes the test:
=P(not flawed and clear inspection)/P(pass the inspection)=(1-0.1)*1/0.90025=0.999722