Refer to Exercise 28. Assume that both inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw.

a. Assume that the probability that an item has a flaw is 0.10. If an item is passed by the first inspector, what is the probability that it actually has a flaw?

b. Assume that the probability that an item has a flaw is 0.10. If an item is passed by both inspectors, what is the probability that it actually has a flaw?

Answer:

Step 1 of 3:

From the given data we have, the two inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw.

Let F denoted the event that an item has a flaw. Let A denote the event that a flaw is detected by the first inspector. Let B denote the event that a flaw is detected by the second inspector.

In exercise 28. We have the probabilities are,

.

Step 2 of 3:

a). We have to find the probability that the flaw is found by a first inspector.

Given that, the probability that an item has a flaw is 0.10. We are given the probabilities,

,

, 1 - 0.7

= 1- 0.9 = 0.3

= 0.1

= 1- 0.1

= 0.9

Using by Bayes rule

=

=

= 0.01

Therefore, the probability that the flaw is found by a first inspector is 0.01.