Question

2. 120 castings are produced by die casting process. The castings are inspected to check their surface roughness and dimensional accuracy. The results from 120 castings are summarized as the following: Dimensional Accuracy good 85 10 Bad 15 10 Surface Roughness High Low Let A denote the event that a casting has high surface roughness, and let B denote the event that a casting has bad dimensional accuracy. Determine the number of castings in a) An B b) An B c) AU B d) A'UB

Answer 1

(a)

	Dimensional Accuracy good (B')	Dimensional accuracy bad (B)	Total
Surface roughness high (A)	85	15	100
Surface roughness low(A')	10	10	20
Total	95	25	120

= Number of castings with high surface roughness AND bad dimensional accuracy = 15

So,

Answer is:

15

(b)

= Number of castings with high surface roughness AND good dimensional accuracy = 85

So,

Answer is:

85

(c)

= Number of castings with high surface roughness OR bad dimensional accuracy

= 100 + 25 - 15

= 110

So,

Answer is:

110

(d)

= Number of castings with low surface roughness OR bad dimensional accuracy

  

= 20 + 25 - 10

= 35

So,

Answer is:

35