The finishing process on new furniture leaves slight blemishes. The table shown below displays a manager’s probability assessment of the number of blemishes in the finish of new furniture.

Number of Blemishes

0

1

2

3

4

5

Probability

0.34

0.25

0.19

0.11

0.07

0.04

Let event *A* be that there are more than three blemishes and let event *B* be that there are four or fewer blemishes. Which of the following statements is true?

A) *P*( A ∩ **B**) = 0.18.

B) *P*(A U **B** ) = 0.07.

C) Events *A* and *B* are collectively exhaustive.

D) Events *A* and *B* are mutually exclusive.

14. Let event *A* be that there are more than two blemishes and let event *B* be that there are four or fewer blemishes. Which of the following statements is true?

A) *P*(A ∩ **B** ) = 0.18.

B) *P*( A U **B**) = 0.07.

C) *P*( Ac ) = 0.58.

D) *P*( BC ) = 0.89.

**15.**Let *A* be the event that there is at least one blemish and let event *B* be that there at most three blemishes. Which of the following statements is true?

A) *P*(A ∩ **B** ) = 0.76.

B) *P*( A U **B**)= 0.55.

C) *P*(Ac ) = 0.30.

D) *P*(BC ) = 0.96.

16. The purchasing agent for a municipality has contracted with a local car dealer to purchase four cars. The dealer has 25 cars on his lot; 10 red, 7 blue, 6 white and 2 purple. If the purchasing agent has no control over the colors he receives, what is the probability that he receives at least one of the purple cars?

A) 0.33

B) 0.30

C) 0.36

D) 0.39

**17. **As the office manager for a medical office with ten doctors, you are responsible for developing the roster for the on-call shift for the next three nights. How many different ways could you assign different doctors to the next three nights?

A) 1020

B) 840

C) 720

D) 640