Problem 1

A large company that must hire a new president prepares a final list of seven candidates, all of whom are equally qualified. Three of these candidates are members of a minority group. To avoid bias in the selection of the candidate, the company decides to select the president by lottery.

1. What is the probability one of the minority candidates is hired?
2. Which method of probability did you use to make this estimate? Explain

Problem 2

Berdine's Chicken Factory has several stores in the Hilton Head, South Carolina, area. When interviewing applicants for server positions, the owner would like to include information on the amount of tip a server can expect to earn per check (or bill). A study of 500 recent checks indicated the server earned the following amounts in tips per 8-hour shift.

Amount of Tip	Number
$0 up to $ 20	200
20 up to 50	100
50 up to 100	75
100 up to 200	75
200 or more	50
Total	500

1. What is the probability of a tip of $200 or more?
2. Are the categories "$0 up to $20," "$20 up to $50," and so on considered mutually exclusive?
3. If the probabilities associated with each outcome were totaled, what would that total be?
4. What is the probability of a tip of up to $50?
5. What is the probability of a tip of less than $200?

Problem 3

There are 100 employees at Kiddie Carts International. Fifty-two of the employees are production workers, 43 are supervisors, 4 are secretaries, and the remaining employee is the president. Suppose an employee is selected:

1. What is the probability the selected employee is a production worker?
2. What is the probability the selected employee is either a production worker or a supervisor?
3. Refer to part (2). Are these events mutually exclusive?
4. What is the probability the selected employee is neither a production worker nor a supervisor?

Problem 4

In a management trainee program at Claremont Enterprises, 60% of the trainees are female and 40% male. Ninety percent of the females attended college, and 70% of the males attended college.

1. A management trainee is selected at random. What is the probability that the person selected is a female who did not attend college? Use the table in part 2 to determine your answers.
2. Create and post the Joint Probability Table.
3. Are gender and attending college independent? Why?Explain
4. Do the joint probabilities total 1.00? Why?

The following is an example using different data:

http://lectures.mhhe.com/connect/0077416724/guided_examples/Chapter05/LGE05-49.mp4

Problem 5

Thirty percent of the homes constructed in the Quail Creek area include a security system. Three homes are selected at random: (Hint: Review the compliment rule)

1. What is the probability all three of the selected homes have a security system?
2. What is the probability none of the three selected homes have a security system?
3. What is the probability at least one of the selected homes has a security system?
4. Did you assume the events to be dependent or independent?

Problem 6

The board of directors of Saner Automatic Door Company consists of 12 members, 5 of whom are women. A new policy and procedures manual is to be written for the company. A committee of 3 is randomly selected from the board to do the writing. (Hint: Conditional Probability)

1. What is the probability that all members of the committee are men?
2. What is the probability that at least 1 member of the committee is a woman? (Hint: Review the compliment rule)