## What proportion of the boards manufactured last month were defective?

1.  Let A and B be events with P(A) = 0.3and P(A ∪ B) = 0.7.

a.  For what value of P(B) will A and B be mutually exclusive?

b.  For what value of P(B) will A and B be independent?

2.   A snowboard manufacturer has three plants, one in the eastern United States, one in the western United States, and one in Canada. Production records show that the U.S. plants each produced 10,000 snowboards last month, while the Canadian plant produced 8000 boards. Of all the boards manufactured in Canada last month, 4% had a defect that caused the boards to delaminate prematurely. Records kept at the U.S. plants show that 3% of the boards manufactured in the eastern United States and 6% of the boards manufactured in the western United States had this defect as well.

a.  What proportion of the boards manufactured last month were defective?

b.  What is the probability that a snowboard is defective and was manufactured in Canada?

c.   Given that a snowboard is defective, what is the probability that it was manufactured in the United States?

### What is the probability that the parcel was shipped express and arrived the next day?

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….

### If a man tests negative, what is the probability that he actually has the disease?

1.  Refer to Example 2.26. a.  If a man tests negative, what is the probability that he actually has the disease? b.  For many medical tests, it is standard procedure….