1. You will submit your HW assignment within Canvas in the Assignments area.  Remember to use naming convention detailed in the syllabus.  Word, Excel, screenshots, .jpegs, .pdfs &/or all types of documents can be submitted.

2. Please include a cover sheet with your name and date, that includes online submissions.

3. Include a short synopsis of the problem, all assumptions, and definitions used at the beginning of each exercise.

4. Answer the problems as completely as possible. Neatness, accuracy, and overall clarity of work are important. Full credit will only be given for problems, which include the aforementioned items. I am looking for process and methodology not necessarily one correct answer.

5. Submit homework by the due date and time.

Remember: You are telling a "story" in the attempt to win a contract from a client, do your best to tell the story, win the contract, and get paid (or in this case get an excellent grade!)

Please submit the following problems:

The same instructions apply for all homework problems. It is vitally important that you do a good job defining the problem, stating assumptions, explaining your analysis, raising questions with regard to TRADE-OFFS, DEFINING RISK, QUANTIFYING RISK, etc., feel free to use graphs, tables, and/or any other means to get your point across. Simply writing an answer down is woefully inadequate (i.e., you will receive no points).

I. Dana University has a unique college football team. The team has many players form the Pacific Islands. Of all the players on the team, 50% are from the mainland U.S., while 20% of the players are from the Hawaiian Islands, 10% of the players are from Tonga, 10% of the players are from Samoa, 5% of the players are from Fiji, and 5% are from Guam. Given that a player is not from the mainland, there is a 90% probability that they are an offensive or defensive lineman. However, given the player is from the mainland U.S. there is only a 20% chance. Please complete the following:

a. Construct a probability tree for this problem

b. Construct a probability table for this problem

c. What is the make-up of the team, lineman vs. non-lineman?

d. If Coach Clem walks into the cafeteria given that he see a lineman, what is the probability that the lineman will be from Samoa?

II.John Woo has decided to purchase a cellular phone for his car, but he is uncertain about which rate plan to select. The "regular" plan charges a fixed fee of $57 per month for 80 minutes of airtime plus $0.33 per minute for any time over 80 minutes. The "executive" plan charges a fixed fee of $77 per month for 110 minutes of air time plus $0.25 per minute over 110 minutes. (HINT: This is a break-even problem and examples of this problem type can be found in Kros Chapter 1, pg 13-20 and the study guide, Chapter 1.)

a. If John expects to use the phone for two hours per month, which plan should he select?

b. Perform an analysis based on the idea that John believes his average use will be two hours per month but knows that he will never use less than one hour or more than three hours per month.

c. How does your decision change if John's usage habits change and now he uses the phone on average four hours a month, but will never use it more than five hours or less than three hours a month?

III. A service station owner receives tires from two sources, plant A and plant B. There is a probability of 60% that tires come from plant A. According to the store owner, 20% of all tires from plant A are defective and only 10% of tires from plant B are defective.

a. Construct a probability tree for this problem

b. Construct a probability table for this problem.

c. Find the probability that a tire comes from plant A and is defective (HINT: find P(plant A and defective)).

d. Given the you find a defective tire, what is the probability that it came from plant B?