1.For two events, M and N, P(M)equals=0.40.4, P(N|M)equals=0.30.3, and P(N|M')equals=0.60.6.

Find P(M'M'|Upper NN).

2.Of all the people applying for a certain job, 85% are qualified and 15%

are not. The personnel manager claims that she approves qualified people 9%

of the time; she approves unqualified people 30%

of the time. Find the probability that a person is qualified if he or she was approved by the manager.

3. A building contractor buys 80% of his cement from supplier A and 20% from supplier B. A total of 90%

of the bags from A arrive undamaged, while 95% of the bags from B arrive undamaged. Find the probability that a

damaged bag is from supplier A.

4. Companies A, B, and C produce 40%, 30%, and 30%,

respectively, of the major appliances sold in a certain area. In that area, 3%

of the company A appliances, 4.5%

of the company B appliances, and 1% of the company C appliances need service within the first year. Suppose a defective appliance is chosen at random; find the probability that it was manufactured by Company B.

5.The probability that a person with certain symptoms has hepatitis is 0.75.

The blood test used to confirm this diagnosis gives positive results for 92%

of people with the disease and 5%

of those without the disease. What is the probability that an individual who has the symptoms and who reacts positively to the test actually has hepatitis?

6.Solve the problem. Express the answer as a percentage.

70% of the workers at Motor Works are female, while 47%

of the workers at City Bank are female. If a worker is selected at random, what is the probability that the worker will be from Motor Works, given that the worker is female? Assume a 50-50 chance of selecting either bank. Round your answer to the nearest tenth, if necessary.

7. Medical researchers developed a test that determines whether a person has a particular disease. The results have produced the following probabilities, where D represents having the disease and N represents a negative test.

P(D'|N)equals=

0.86. and P(D|N')equals=0.73. Assuming that P(N')equals=0.09. , find P(N'|D).

8. In a county, 46% of the adults are males. One adult is randomly selected for a survey involving credit card usage.

a. Find the prior probability that the selected person is a female.

b. It is later learned that the selected survey subject was smoking a cigar. Also, 8.8%

of males smoke cigars, whereas 2.9% of females smoke cigars. Use this additional information to find the probability that the selected subject is female.