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 729 that were judged defective, inspector B found 757 such joints, and 922 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

Solution:-

P(A) = 729/10,000 = 0.0729

P(B) = 757/10,000 = 0.07570

P(A or B) = 0.0922

a) The probability that the selected joint was judged to be defective by neither of the two inspectors is 0.9078.

P(Aor B) = 0.0922

The probability that selected joint was judged to be defective by neither of the two inspectors = P(Aor B)c

P(Aor B)c = 1 - P(Aor B)

P(Aor B)c = 1 - 0.0922 = 0.9078

b) The probability that the selected joint was judged to be defective by inspector B but not by inspector A = 0.0193.

P(Aor B) = P(A) + P(B) - P(Aand B)

0.0922 = 0.0729 + 0.0757 - P(A and B)

P(A and B) = 0.1486 - 0.0922

P(A and B) = 0.05640

The probability that the selected joint was judged to be defective by inspector B but not by inspector A = P(only B) P(only B) = P(B) - P(A and B)

P(only B) = 0.0757 - 0.0564

P(only B) = 0.0193

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