Probability
Probability
IP 4
In a large batch, 10% of components are defective.
An inspection flags:
a defective component with probability \(0.8\);
a non-defective component with probability \(0.1\).
The same component is inspected twice. Conditional on its true defect status, the two inspection results are independent.
Find the probability that it is flagged twice.
Given two flags, find the probability that it is defective.
Compare this with the probability of a defect given just one flag.
Solution:
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Answer:(a) \(0.073\).
(b) \(\frac{64}{73}\).
(c) One flag gives \(\frac8{17}\). Since \(\frac{64}{73}>\frac8{17}\), two flags give a higher probability of a defect.
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