A particular electronic component is produced at two plants for an electronics manufacturer.Plant A produces 70% of the components used and the remainder are produced by plant B.The probability that a component is defective is 0.02 if it is produced at plant A and 0.01 if it is produced at plant B.The probability that the component is defective is ______
A)0.3
B)0.01
C)0.003
D)0.176
E)0.017

Question

Quizplus · Accepted Answer

To find the overall probability that a component is defective, we use the law of total probability. The probability that a component is defective given that it's from Plant A is 0.02, and from Plant B is 0.01. Since 70% of the components are from Plant A and 30% from Plant B, the total probability is (0.7 * 0.02) + (0.3 * 0.01) = 0.014 + 0.003 = 0.017.

A Particular Electronic Component Is Produced at Two Plants for an Electronics