Items are inspected for flaws by two quality inspectors. If a flaw is present, it will be detected by the first inspector with probability 0.9. and by the second inspector with probability 0.7. Assume the inspectors function independently.

a. If an item has a flaw, what is the probability that it will be found by both inspectors?

b. If an item has a flaw, what is the probability that it will be found by at least one of the two inspectors?

c. Assume that the second inspector examines only those items that have been passed by the first inspector. If an item has a flaw, what is the probability that the second inspector will find it?

Answer:

Step 1 of 4:

Given that the items are inspected for flaws by two quality inspectors.

Let A denote the event that the flaw is found by the first inspector.

Let B denote the event that the flaw is found by the second inspector.

Then,

.

Step 2 of 4:

a). The aim is to find the probability that the flaw is found by both inspector.

That is,

= 0.9

= 0.63

Therefore, the probability that the flaw is found by both inspector is 0.63.