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 Computations1

. A restauraunt offers the following limited lunch menu:Main CourseHamChickenFishVeggie Burger VegetablesPotatoesPeasSalad BeveragesCoffeeTeaMilkSoda DessertsCakePieIce Cream

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 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 9th grade Some High School H

.S

. Graduate Some College Assoc

. Degree Bach

. Degree Advanced DegreeMale 6

.3 9

.1 28

.1 18

.6 6

.4 16

.7 10

.2Female 6

.4 8

.9 30

.3 21

.1 8

.3 17

.6 9

.7Total 12

.7 18

.0 58

.5 39

.8 14

.6 34

.2 20

.0What is the probability that a randomly selected American, aged 25 or over,(a) (2 point) …

. has an advanced degree?

Answer (Show your work): (b) (1 point) … is female?

Answer (Show your work): (c) (1 point) …

. is a female with an advanded degree?Answer (Show your work): (d) (1 point) … has attended college (may or may not have graduated)?Answer (Show your work):

3

. You are in charge of planning a Talent Show for your daughter’s Elementary School

. The following teachers at the school have agreed to show off their talents, as follows:• Clown Act – Mrs

. Barbour• Playing Trombone – Mrs

. McDonnell• Knock-Knock Jokes – Mrs

. Peck• Singing the ABC Song – Mrs

. Santoro• Mime – Mrs

. Fisher• Magic Act – Mr

. Annesi• Singing “Somewhere Over the Rainbow” - Mr

. Bella

. (1 point) You need to select 3 of the teachers to perform in the first act

. How many different ways can you select the 3 teachers?Answer: Explanation:b

. (1 point) You need to select 3 of the teachers to perform in the first act

. How many different ways can you select 3 teachers and schedule them for the first act?Answer: Explanation:4

. Let’s say your sister is having a baby and you are talking with her about whether you think it will be a boy or a girl

. She doesn’t know the gender of the baby

. Determine whether the following statements of probability are considered classical, empirical, or subjective probability

. Explain how you know which type of probability it is

. Note: You do not need to compute the actual probability

.a

. (1 point) There are two elementary schools in town where your sister lives, with students randomly selected to attend

. One school is much larger than the other, so many more students attend School A than the students attend School B

. The probability that the child will attend School A

.Answer:

.b

. (1 point) The probability that your sister will have a boy

.Answer:

c

. (1 point) Children in the town where your sister lives have a choice of playing one of three sports: (a) Soccer (b) Lacrosse and (c) Swimming

. The probability that the child will participate in swimming

.Answer:

d

. (1 point) The probability that the baby will be born on a Friday

.Answer: Part II

. Case Study The case of the Carribean Criminals

This week Patty Madeye is helping the script-writers on a case of embezzlement at a local law practice, Dewey, Cheatem, and Howe

. [Get it?]

The characters of the “Patty Madeye Mysteries” will be investigating a case of embezzlement planned and executed by a team of 2 people who work at the law firm

. The story goes that the male/female pair of criminals are both married (to other people) but involved in a love-affair with each other

. They have stolen over $2 million in funds from company accounts and have disappeared to somewhere in the Carribean

. Your job will be to use your knowledge of probability and counting methods to help the writers identify possible candidates to be written into the script

. Name Gender Position StatusKelly Female Specialist MarriedAndrea Female Attorney SingleAshley Female Associate SingleBruce Male Attorney-Partner SingleSerge Male Specialist MarriedKaren Female Paralegal SingleAmy Female Specialist MarriedMarion Female Attorney SingleJames Male Attorney-Partner MarriedJanice Female Specialist MarriedLori Female Associate SingleTimothy Male Associate MarriedRobert Male Attorney-Partner SingleMary Female Paralegal MarriedEric Male Attorney-Partner SingleStephanie Female Attorney-Partner SingleDana Female Associate MarriedJoseph Male Associate MarriedKathleen Female Attorney SingleCarissa Female Associate SingleDon Male Specialist MarriedMichael Male Attorney-Partner MarriedAnne Female Specialist SingleScott Male Attorney-Partner SingleWilliam Male Associate MarriedJohn Male Attorney MarriedPenny Female Associate SingleElaine Female Specialist SingleDaniel Male Associate MarriedJustin Male Attorney MarriedTask #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)

.