2-27. Samples of a cast aluminum part are classified on the basis of surface fin

Question

2-27. Samples of a cast aluminum part are classified on the basis of surface finish (in microinches) and edge finish. The results of 100 parts are summarized as follows: edge finish excellent 80 10 good surface finish excellent good (a) Let A denote the event that a sample has excellent surface finish, and let B denote the event that a sample has excel lent edge finish. Determine the number of samples in A' n B, B', and A U B. (b) Assume that each of two samples is to be classified on the basis of surface finish, either excellent or good, and on the basis of edge finish, either excellent or good. Use a tree diagram to represent the possible outcomes of this experiment.

Explanation / Answer

Part (a)

(A’ B) represents good surface finish and excellent edge finish.

Hence, n(A’ B) = 10 ANSWER 1

B’ represents good surface finish. Hence, n(B’) = 2 + 8 = 10 ANSWER 2

n(A B) = n(A) + n( B) - n(A B) = 82 + 90 – 80 = 92 ANSWER 3

Part (b)

Possible outcomes are:

Possibility

Sample 1

Sample 2

Surface finish

Excellent

Excellent

Surface finish

Excellent

Good

Surface finish

Good

Excellent

Surface finish

Good

Good

Edge finish

Excellent

Excellent

Edge finish

Excellent

Good

Edge finish

Good

Excellent

Edge finish

Good

Good

DONE

Possibility

Sample 1

Sample 2

Surface finish

Excellent

Excellent

Surface finish

Excellent

Good

Surface finish

Good

Excellent

Surface finish

Good

Good

Edge finish

Excellent

Excellent

Edge finish

Excellent

Good

Edge finish

Good

Excellent

Edge finish

Good

Good

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