Unit 3: Probability and Counting Rules - Assignment

Total points for Assignment: 35 points.

Assignments must be submitted as a Microsoft Word document and uploaded to the Dropbox for Unit 3.
All Assignments are due by Tuesday at 11:59 PM ET of the assigned Unit.
NOTE: Assignment problems should not be posted to the Discussion threads. Questions on the Assignment problems should be addressed to the instructor by sending an email or by attending office hours.
You must show your work on all problems. If a problem is worth 2 points and you only show the answer, then you will receive only 1 point credit. If you use a calculator or online website, give the source and tell me exactly what you provided as input. For example, if you used Excel to compute 16 * 16, tell me “I typed =16*16 into Excel and got 256. You may type your answer right into this document.

Part I. Basic Computations
1. A restauraunt offers the following limited lunch menu:
|Main Course |Vegetables |Beverages |Desserts |
|Ham |Potatoes |Coffee |Cake |
|Chicken |Peas |Tea |Pie |
|Fish |Salad |Milk |Ice Cream |
|Veggie Burger | |Soda | |

a. (2 points) If one item is selected from each of the four groups, how many different meals can you order? Answer: Explanation: b. (2 point) If you don’t order a dessert, how does your answer change? Answer: Explanation:

2. According to the American FactFinder website[1] there were 197.8 million adults over the age of 25 in the United States in 2007. The table below shows the educational attainment for these adults. Use the data in the table, expressed in millions, to solve the following problems.
| |Less than |Some High School |H.S. |
| |9th grade | |Graduate |
|Kelly |Female |Specialist |Married |
|Andrea |Female |Attorney |Single |
|Ashley |Female |Associate |Single |
|Bruce |Male |Attorney-Partner |Single |
|Serge |Male |Specialist |Married |
|Karen |Female |Paralegal |Single |
|Amy |Female |Specialist |Married |
|Marion |Female |Attorney |Single |
|James |Male |Attorney-Partner |Married |
|Janice |Female |Specialist |Married |
|Lori |Female |Associate |Single |
|Timothy |Male |Associate |Married |
|Robert |Male |Attorney-Partner |Single |
|Mary |Female |Paralegal |Married |
|Eric |Male |Attorney-Partner |Single |
|Stephanie |Female |Attorney-Partner |Single |
|Dana |Female |Associate |Married |
|Joseph |Male |Associate |Married |
|Kathleen |Female |Attorney |Single |
|Carissa |Female |Associate |Single |
|Don |Male |Specialist |Married |
|Michael |Male |Attorney-Partner |Married |
|Anne |Female |Specialist |Single |
|Scott |Male |Attorney-Partner |Single |
|William |Male |Associate |Married |
|John |Male |Attorney |Married |
|Penny |Female |Associate |Single |
|Elaine |Female |Specialist |Single |
|Daniel |Male |Associate |Married |
|Justin |Male |Attorney |Married |

Task #1: In your first meeting with the writers, they show you the list of the character sketches for the employees that work at the law practice.

The writers think that the male embezzler should be one of the partners of the law firm, indicated in this list by “Attorney-Partner”. For the female embezzler, they have chosen someone who is listed as a “Specialist”. Specialists are employees of the firm who offer subject-matter expertise in specific areas such as real estate or accounting.

a. (4 points) How many different choices do we have for the male/female team of embezzlers?
[Remember: both members of the team are married.]

Answer:
Explanation:

b. (4 points) How would this answer be different if the 2 members of the male/female team don’t have to be married? In other words, they could be either single or married.

Answer:
Explanation:

Task #2: (4 points) The writers want to include an accomplice in the story – that would be someone else in the firm who knew that the pair were stealing from the company.

If the accomplice is selected at random from the remaining employees, what is the probability that the accomplice is female?

Answer:
Explanation:

Task #3 (8 points) – Who should be the “whistle-blower”?

The writers of the show have asked you to think of a “plot-twist” that can be solved using probability. For example, let’s say that someone claims that there’s a 50% chance that the “Attorney-Partner” embezzler is male but that would only be the case if there were an equal number of males and females.

Using the evidence from above and what you have learned about probability, in a well-structured essay, present a problem and its solution. Be creative!!

Answer:

Requirements - Write your essay in this document – do not save it in a separate file. - You must clearly state your position in 2-3 well-structured paragraphs using proper grammar, spelling, and sentence structure. - This is not an “opinion” question – you must offer evidence from the data or your knowledge of probability. - Don’t forget to explain how the problem can be solved with probability. (Remember, the script writers haven’t taken this class yet).
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[1] American FactFinder - 2006-2008 American Community Survey 3-Year Estimates. (2010). Retrieved September 22, 2010 from U.S. Census Bureau, United States - Educational Attainment: http://factfinder.census.gov.