Question

one hundred castings were inspected for defects and 85 were found to be free of defects. among the 15 defective castings, 9 were found to have blowholes and 12 were found to have sand inclusions. a).How many castings have exactly one type of defect? b) How many castings have at least one type of defect? c) How many castings have both types of defects?

Answer 1

here let number of casting with blowholes and sand inclusions are A and B

therefore from above N(A)=9 ; N(B)=12 and N(A u B)=15

therefore N(A n B)=N(A)+N(B)-N(A u B)=9+12-15=6

a) castings have exactly one type of defect =N(A)+N(B)-2*N(A n B)=9+12-2*6=9

b)

castings have at least one type of defect N(A u B) =15

c)

castings have both types of defects =N(A n B)=6