Human visual inspection of solder joints on printed circuit boards can be very s

Question

Human visual inspection of solder joints on printed circuit boards can be very subjective. Part of the problem stems from the numerous types of solder defects (e.g., pad nonwetting, knee visibility, voids) and even the degree to which a joint possesses one or more of these defects. Consequently, even highly trained inspectors can disagree on the disposition of a particular joint. In one batch of 10,000 joints, inspector A found 747 that were judged defective, inspector B found 748 such joints, and 1113 of the joints were judged defective by at least one of the inspectors. Suppose that one of the 10,000 joints is randomly selected.

(a) What is the probability that the selected joint was judged to be defective by neither of the two inspectors?

(b) What is the probability that the selected joint was judged to be defective by inspector B but not by inspector A?

Explanation / Answer

P(Inspector A found judged defective) = 0.0747

P(Inspector B found judged defective) = 0.0748

P(At least one of them found judged defective) = 0.1113

So,

a) P(Neither of two found judged defective)

= 1 - P(At least one of them found judged defective)

= 1 - 0.1113

= 0.8887

b) P(Both found judged defective) = 0.0747 + 0.0748 - 0.1113 = 0.0382

Hence,

P(Inspector B found judged defective but not inspector A) = 0.0748 - 0.0382 = 0.0366

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