Samples of a cast aluminum part are classified on the basis of surface finish (i

Question

Samples of a cast aluminum part are classified on the basis of surface finish (in microinches) and lengtih measurements. The results of 100 parts are summarized as follows: Length Good Surface Excellent Finish Good Excellent 80 10 Let A denote the event that a sample has excellent surface finish, and let B denote the event that a ple has excellent length. Determine: (e) If the selected part has excellent surface finish, what is the probability that the length is excellent? (f) If the selected part has good length, what is the probability that the surface finish is excellent?

Explanation / Answer

a) P(A) = (80 + 2) / 100 = 0.82

b) P(B) = (80 + 10) /100 = 0.90

c) P(A | B)= P(A n B) / B = (80 / 100) / (90 / 100) = 80/90 = 0.889

d) P(B | A) = P(A n B) / A = (80 / 100) / (82 / 100) = 80/82 = 0.976

e) P(B | A) = 0.976

f) P(A | B') = P(B' | A) * P(A) / P(B)

                 = (1 - 0.976) * 0.82 / 0.9

                 = 0.0219

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