(need help with the highlighted ones C, D, and F) Samples of a cast aluminum par

Question

(need help with the highlighted ones C, D, and F)

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: 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

c) P(A given B) =P(A and B)/P(B)= 80/(80+10)= 0.889

d) P(B given A)=P(A and B)/P(A)=80/(80+2)=0.9756

f) P( excellent surface given that the length is good) =P(excellent surface and length is good)/ P(length is good)

=2/ (2+8) =0.2

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