1. In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective,….

## Given that the test is positive, what is the probability that the person has the disease?

1. 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 aflaw?

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?

2. Refer to Example 2.26. Assume that the proportion of people in the community who have the disease is 0.05.

a. Given that the test is positive, what is the probability that the person has the disease?

b. Given that the test is negative, what is the probability that the person does not have the disease?