Answer to Question #236657 in Statistics and Probability for Steve

Question

All products on an assembly line must pass two inspections. It has been determined that
the probability that the first inspector will miss a defective item is 0.09. If a defective
it is 0.01. What is the probability that a defective item will not be rejected by either
item gets past the first inspector, the probability that the second inspector will not detect
inspector? (All good items pass both inspections.)

Answer 1

What is the probability that a defective item will pass by both inspectors?

$$P(\text{defective pass both})=P(\text{pass first}\cap \text{pass second})$$

$$=P(\text{pass first})\cdot P(\text{pass second }|\text{passed\ first})$$

$$=0.09(0.01)=0.0009$$