probability of two people missing a defective item on an assembly line?

Question

An assembly line has two inspectors. The probability that the first inspector will miss a defective item is 0.05. If the defective item passes the first inspector, the probability that the second inspector will miss it is 0.01. What is the probability that a defective item will pass by both inspectors?

Answer 1

The probability that two things happen is the probability of each thing happening on their own multiplied together. You're looking for the probability that both inspectors will miss a defective item, which are both given to be 0.05 and 0.01. Therefore, you multiply 0.05 × 0.01 = 0.0005. The probability that a defective item will pass by both inspectors is 0.0005.