2-102. +Samples of a cast aluminum part are classified on the basis of surface f

Question

2-102. +Samples of a cast aluminum part are classified on the basis of surface finish (in microinches) and length measurements. The results of 100 parts are summarized as follows: Length Good Excellent 80 10 Surface Excellent Finish Good Let A denote the event that a sample has excellent surface finish, and let B denote the event that a sample has excellent length. Determine: (a) P(A) (c) P(AIB) d) P BIA) (b) P(B) (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/(80+2) = 82/100 = 0.82. (Ans).

(b) P(B) = 80/(80+10) = 90/100 = 0.90. (Ans).

(c) P(A | B) = P(AB) / P(B) = (80/100) / (90/100) = 0.8889. (Ans).

(d) P(B | A) = P(A | B) * P(B) / P(A) = (0.8889 * 0.9) / 0.82 = 0.9756. (Ans).

(e) The required probability that if a given selected part has excellent surface finish, the length is excellent = P(B | A) = 0.9756. (Ans).

(f)The required probability that if a given selected part has excellent length, the surface finish is excellent = P(A | B) = 0.8889. (Ans).

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