Answer to Question #248125 in Statistics and Probability for Ch@nce

Question

It has been determined that

the probability that the first inspector will miss a defective item is 0.09. If a defective

item gets past the first inspector, the probability that the second inspector will not detect

it is 0.01. What is the probability that a defective item will not be rejected by either

inspector

Answer 1

$$P(\text{defective pass both})=P(\text{pass first}\cap \text{pass second})$$ $$=P(\text{pass first})\cdot P(\text{pass second }|\text{passed\ first})$$ $$=0.09(0.01)=0.0009$$