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

Question

Samples of a cast aluminium part are classified on the basis of surface finish (in micro inches) and length measurements. The results of 100 parts are summarized as follows: Length Excellent Good Surface Excellent 80 2 Finish Good 10 8 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) (b) P(B) (c) P(A | B) (d) P(B | A) (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 = 0.9

C) P(A|B) = P(A and B) /P(B) = (80/100)/0.9 = 0.89

D) P(B|A) = P(A and B)/P(A) = (80/100)/0.82 = 0.98

E) P(excellent length | excellent surface finish) = P(B | A) = 0.98

F) P(excellent surface finish|good length) = P(excellent surface finish and good length) /P(good length)

= (2/100)/((2+8)/100)

= 0.2

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