Question

A factory makes cylindrical workpieces. The turning and milling operations are independent. Based on past experiences, under normal circumstances, 1% of turned workpieces, and 2% of milled workpieces were defective.

Assume that one workpiece is randomly selected from a lot of turned and milled workpieces.

a) What is the probability that at least one of the operations (turning and milling) will be defective?

b) What is the probability that in a production lot of 10 workpieces, none of the workpiece is defective?

c) What is the expected number of defective workpiece in a production lot of 15 workpieces? What is the standard deviation?

Answer 1

P(A U B) = P(A) + P(B) - P(A B)

For independent events, P(A B) = P(A) x P(B)

a) P(at least one of the operation is defective) = P(turning is defective) + P(milling is defective) - P(both are defective)

= 0.01 + 0.02 - 0.01x0.02

= 0.0298

b) P(none of the 10 pieces are defective) = [P(not defective)]¹⁰

= [1 - P(defective)]¹⁰

= (1 - 0.0298)¹⁰

= 0.7389

c) n = 15

P(defective), p = 0.0298

Mean number of defective work pieces = np

= 15 x 0.0298

= 0.447

Standard deviation =

=

= 0.6585