Statistics and Risk Management - data.cteunt.orgdata.cteunt.org/content/files/finance/statistics-risk-management/...Statistics and Risk Management Basic Probability Performance Objective:

Copyright © Texas Education Agency, 2012. All rights reserved. 1

Statistics and Risk Management Basic Probability

Performance Objective:

After completing this lesson, the student will understand the importance and demonstrate competencies of being able to select the appropriate method and calculate basic probability problems.

Approximate Time: When taught as written, this lesson should take 8-10 days to complete.

Specific Objectives: The student will discuss the importance of probability.

The student will understand some basic terms and concepts of probability. The student will see and understand the basic types of calculations used.

This lesson corresponds with Unit 5 of the Statistics and Risk

Management Scope and Sequence.


TEKS Correlations: This lesson, as published, correlates to the following TEKS for Basic Probability. Any changes/alterations to the activities may result in the elimination of any or all of the TEKS listed. 130.169 (C) (6) (G) … apply the common rules of probability to evaluate business alternatives… InterdisciplinaryTEKS: English: 110.31 (C) (21) (B) … organize information gathered from multiple sources to create a variety of graphics and forms (e.g., notes, learning logs)… 110.31 (C) (22) (B) …evaluate the relevance of information to the topic and determine the reliability, validity, and accuracy of sources (including Internet sources) by examining their authority and objectivity… 110.31 (C) (23) (C) … use graphics and illustrations to help explain concepts where appropriate… 110.31 (C) (23) (D) … use a variety of evaluative tools (e.g., self-made rubrics, peer reviews, teacher and expert evaluations) to examine the quality of the research…


Math: 111.36 (C) (4) (A) … compare theoretical and empirical probability; 111.37. (C) (3) (B) … use probabilities to make and justify decisions about risks in everyday life

Occupational Correlation (O*Net - http://www.onetonline.org/)

Statisticians 15-2041.00 Similar Job Titles: Statistical Analyst, Education Research Analyst, Research Associate, Clinical Biostatistics Director, Clinical Statistics Manager, Institutional Research Director, Program Research Specialist, Research Analyst, Statistical Reporting Analyst Tasks:

Report results of statistical analyses, including information in the form of graphs, charts, and tables.

Process large amounts of data for statistical modeling and graphic analysis, using computers.

Identify relationships and trends in data, as well as any factors that could affect the results of research.

(Soft) Skills: Deductive reasoning; Written comprehension; Problem sensitivity; Originality

http://www.onetonline.org/


Instructional Aids: 1. Display for presentation, websites for

assignments and class discussion 2. Assignment Worksheets 3. Supporting Spreadsheets

Materials Needed: 1. Printer paper 2. Assignments and website information ready to distribute to

students.

Student projects will be displayed to increase interest in Statistics

Equipment Needed: 1. Computer with presentation and Internet Access 2. Computers for Students to Conduct Research and Collect Data

for Projects


References:

http://www.khanacademy.org/#statistics Khan Academy: Basic Probability http://www.khanacademy.org/math/probability/v/basic-probability Bayes’ Theorem Through this paper by Mario F. Triola teachers can gain a deeper understanding of the concept of Bayes’ Theorem that they can pass on to their students. With in-depth definitions and examples, teachers will be able to take what is learned and present it to students on a high school level. http://faculty.washington.edu/tamre/BayesTheorem.pdf Introduction to Statistics http://people.hofstra.edu/Stefan_Waner/tutorialsf2/unit6_2.html Probability and Statistics Vocabulary Words http://online.math.uh.edu/MiddleSchool/Vocabulary/Prob_StatVocab.pdf Basic Probability Concepts This site provides an in-depth explanation of how probability problems are solved when using a die. The detailed example experiment can be taken and used in the classroom to explain die probability problems in an easily comprehended way. http://www.onemathematicalcat.org/Math/Algebra_II_obj/basic_probability.htm

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http://www.khanacademy.org/#statistics

http://www.khanacademy.org/math/probability/v/basic-probability

http://www.khanacademy.org/math/probability/v/basic-probability

http://faculty.washington.edu/tamre/BayesTheorem.pdf

http://faculty.washington.edu/tamre/BayesTheorem.pdf

http://people.hofstra.edu/Stefan_Waner/tutorialsf2/unit6_2.html

http://people.hofstra.edu/Stefan_Waner/tutorialsf2/unit6_2.html

http://www.onemathematicalcat.org/Math/Algebra_II_obj/basic_probability.htm

http://online.math.uh.edu/MiddleSchool/Vocabulary/Prob_StatVocab.pdf




Teacher Preparation: Teacher will:

1. Review terms in outline, presentation, and handouts.

2. Locate and evaluate various resources and websites.

3. Have assignments and websites ready.

Learner Preparation: Break the boring barrier. Probability can be fun and definitely interesting. Find examples the student might find interesting; understanding gaming, designing games, evaluating decision on an ongoing basis.

Introduction: STUDENTS will watch the Unit video found here: http:// jukebox.esc13.net/untdeveloper/Videos/Basic%20Probability.mov

STUDENTS will take the practice test and review using the Key, found in Common/Student Documents. EXHIBIT: Excitement for Probability and Learning INTRODUCE: Probability affords the opportunity to improve

decision making and to make persuasive arguments for your decision selection.

ASK: Ask students to express how they arrive at

important decisions like selecting a college or buying a car.


I. What is Probability? A. The probability of a random

event denotes the relative frequency of occurrence of an experiment's outcome, when repeating the experiment.

B. Frequentists consider probability to be the relative frequency "in the long run" of outcomes.

II. Why Probability? A. Probability theory is applied

in everyday life in risk assessment and in trade on commodity markets, and the gaming industry.

B. Governments typically apply probabilistic methods in environmental regulation, where it is called pathway analysis.

III. Analytical Method IV. Probability to Odds V. Results p =

A. 0.0 Not going to happen B. 1.0 It will happen every time C. ??? Somewhere in between

VI. Events A. Independent Events B. Mutually Exclusive C. Exhaustive (No More)

VII. Geometry A. A point is selected at

random in the RED/BLUE square. Calculate the probability that it lies in the BLUE triangle.

VIII. Provide Assignment sheets and discuss and answer any questions about assignment (In class or take home-Instructor’s Option)

IX. Not Always Simple A. Sometimes groups need to

be combined. B. Additive Rule

Use presentation and

BasicProbability_Intro.pptx

http://en.wikipedia.org/wiki/Risk

http://en.wikipedia.org/wiki/Commodity_markets



http://en.wikipedia.org/wiki/Environmental_regulation


X. Problems A. Flip a Coin Once B. Probability it will be Heads.

XI. Flip a Coin Twice a. Probability it will be Heads

Twice. b. Problems

XII. Roll a Pair of Dice a. Probability it will be a pair of

Sixes. XIII. Provide Assignment sheets and

discuss and answer any questions about assignment (In class or take home-Instructor’s Option)

XIV.Bayes’ Theorem a. Thomas Bayes 18th century b. How to accumulate

information and revise estimates of Probability.

XV. Example a. Your Portfolio Manager

suggests that you buy 2000 shares of Acme Production.

B. All of the shares you have bought as per his suggestion have done

C. 100% Probability this is good

D. Example a. You research the

industry and find out this industry on a whole is on a downward spiral

b. Now you adjust the probability this will be a good investment

E. 60% Probability this is good

XVIII. Example A. You research this Specific

Company and find out it is restructuring and struggling.

B. You again adjust the probability this will be a good investment

C. 40% Probability this is good

Provided .docx files

4.1a

BasicProbabilty_Intro.docx


BasicProbability_Rules.pptx

Provided .docx files

4.2a

BasicProbabiltiy_Rules.docx


BasicProbability_Bayes.pptx


XIX.Example A. You call your Broker and

she explains that one of the product lines makes it a prime candidate for a takeover. She knows of several large firms which are publicly examining this company.

B. You again adjust the probability this will be a good investment

C. 80% Probability this is good. D. Known Risk

XX. You Buy • Assessing Knowns

p(Broker is Reliable) = p(YB) =

100%

p(Industry is Sad) = p(NB) = 50%

p(Company is teetering) = p(NB) =

70%

p(Target for Takeover) = p(YB) =

50%

• Formula

XXI.Provide Assignment sheets and

discuss and answer any questions about assignment (In class or take home-Instructor’s Option)


BasicProbability_Bayes.pptx

Provided .docx files 4.3a BasicProbability_Bayes.docx


Guided Practice: See teaching outline.

Independent Practice: See teaching outline.

Review: Question: What are some main uses of probability computations?

Question: Can you describe Bayes’ Theorem?

Informal Assessment: Instructor should observe student discussion and monitor interaction.

Formal Assessment: Completion of provided assignments using included rubrics for grading.


Student Assignment

4.1a Basic Probability Introduction

Key

You need to call your father while he is at work today. He will work 8

hours, but he has total of 2 hours in various unscheduled meetings. He

cannot be disturbed when he is in a meeting. What is the probability that

you will be able to talk with him when you call today.

p(t)= ANSWER: .75 6f/(2m+6f)=.75

You are touring a Ford Plant. Every hour 1 Red, 1 White, 2 Gold, 6

Silver, 2 Blue pickups roll off the assembly line in a random order. What

is the probability of seeing a Silver Pickup roll off the line if you can

spend 5 minutes where they roll off the line before you enter the plant

and see how they are built.

p(s)= ANSWER: .50 6s/(1r+1w+2g+6s+2b)=.50


Student Assignment

4.2a Basic Probability Rules

Key

Revisiting Ford, all year long every hour 1 Red, 1 White, 2 Gold, 6 Silver, 2

Blue pickups roll off the assembly line.

You own a body shop and want to stock paint for auto repairs on Ford

Trucks. You chose to stock Silver, Gold, and Blue.

If needed you will order the Red or White paint on an “AS NEEDED” basis.

What is the probability that you will have the paint in stock when the next

new wrecked Ford pickup is towed to your shop?

p(c)= ANSWER: .83 (2g+6s+2b) / (1r+1w+2g+6s+2b)=.83

Explain how you figured out the probability.

ANSWER: I had to assume that the probability of a wrecked auto would

match production data probabilities in color.


Student Assignment

4.3a Basic Probability Bayes’ Theorem

ANSWER: = .95 x .10 / (.95 x .10) + ( .08 x .90) = .095 / .095 + .072 = .095 / 1.67 = .056

Doctor is correct thinking it is the FLU? (YES) or (NO)

Answer: Yes the doctor is correct it is a probability of only about 6%

that the child with the rash has MEASLES.


Basic Probability Test

Name:______________________

MATCHING

A. Outcomes

B. Survey

C. Event

D. Sample Space

E. Independent Event

F. Random

G. Tree Diagram

H. Sample

I. Probability

1.__________ A randomly-selected group that is used to represent a whole population

2.__________ A diagram used to show the total number of possible outcomes in a probability experiment

3.__________Two or more events in which the outcome of one event does not affect the outcome(s) of

the other event(s).

4.__________The set of all possible outcomes in a probability experiment

5.__________A specific outcome or type of outcome

6.__________A measure of the likelihood of a random phenomenon or chance behavior.

7._________ _ A variety of outcomes that are equally likely to occur

8.__________ A question or set of questions designed to collect data about a specific group of people

9.__________Possible results of a probability event

10. What is the probability of choosing a green marble from a jar containing 5 red, 6 green, and 4 blue

marbles?

11. It is determined that over a 1-year period, 17% of cars will need to be repaired once, 7% will need repairs

twice, and 4% will require three or more repairs. What is the probability that a car chose at random will

need:

a. no repairs?_______

b. no more than one repair?__________

c. some repairs?__________

12. What is the probability of choosing an ace from a standard deck of playing cards?



Name:______________________

13. What is the probability of getting a 0 after rolling a single die numbered 1 to 6?

14. You roll a die three times. What is the probability that:

a. You roll all 6’s?

b. None of your rolls gets a number divisible by 3?

c. The numbers you roll are not all 5’s?

d. You roll all odd numbers?

e. You roll at least one 5?

15. What is the probability of drawing a shell button if there are 5 white buttons, 4 shell buttons, and 3 black

buttons?

16. What is the probability of getting an odd number when rolling a single 6-sided die?

17. You are hungry for M & M’s. If the bag is made up of 20% yellows, 20% red, and orange, blue, and green

each make up 10%. The rest are brown.

If you pick an M & M at random, what is the probability that:

a. It is brown?

b. It is yellow or orange?

c. It is not green?

d. It is striped?

If you pick three M & M’s in a row, what is the probability that:

a. They are all brown?

b. The third one is the first one that’s read?

c. None are yellow?

d. At least one is green?

18. In a probability model, the sum of the probabilities of all outcomes must equal ______.

19. Color Probability

Red 0.3

Green 0.15

Blue 0

Brown 0.15

Yellow 0.2

Orange 0.2

Is the above chart a probability model? ________ What do we call the outcome for “blue?” ________



Name:______________________

20. What is the probability of choosing a vowel from the alphabet?

a. 21/26

b. 5/26

c. 1/21

d. None of the above

21. In a high school statistics class, there are 15 juniors and 10 seniors. Four juniors and five seniors are boys.

If a student is selected at random, what is the probability of selecting a junior or a boy?

a. 24/25

b. 4/5

c. 1/5


22. Which of the following is an impossible event?

a. Choosing an odd number from 1 to 10

b. Getting an even number after rolling a single 6-sided die

c. Choosing a white marble from a jar of 25 green marbles


23. Which of the following is a certain event?

a. Finding a person you know in a room full of people

b. Choosing an odd number from the numbers 1 to 10

c. Getting a 4 after rolling a single 6-sided die


24. A city survey found that 47% of teenagers have a part-time job. The same survey found that 78% plan to

attend college. If a teenager is chosen at random, what is the probability that the teenager has a part-time

job and plans to attend college?

a. 60%

b. 63%

c. 37%


25. In a shipment of 100 televisions, 6 are defective. If a person buys two televisions from that shipment,

what is the probability that both are defective?

a. 3/100

b. 9/2500

c. 1/330




Name:______________________

MATCHING

A. Experiment

B. Outcome

C. Event

D. Probability

26.__________ The measure of how likely an event is

27.__________One or more outcomes of an experiment

28.__________ The result of a single trial of an experiment

29.__________A situation involving chance or probability that leads to results called outcomes

30. Which of the following is an experiment?

A. Tossing a coin

B. Rolling a single 6-sided die

C. Choosing a marble from a jar

D. All of the above

31. Which of the following is an outcome?

A. Rolling a pair of dice

B. Landing on red

C. Choosing 2 marbles from a jar

D. None of the above.

32. Which of the following experiments does NOT have equally likely outcomes?

A. Toss a coin

B. Choose a number at random from 1-8

C. Choose a letter at random from the word SCHOOL

D. None of the above


Basic Probability Test Key

1. H

2. G

3. E

4. D

5. C

6. I

7. F

8. B

9. A

10. 6/15 = 2/5

11. a. .72 b. .89 c. 028

12. 4/52 = 1/13

13. 0/6

14. a. .0046 b. .0125 c. .296 d. .421 e. .995

15. 4/12 = 1/3

16. 3/6 = ½

17. a. .30 b. .30 c. .90 d. 0 Part 2, a. .27 b. .128 c. .512 d. .271

18. One

19. Yes, it equals to 1 Impossible event

20. B

21. B

22. C

23. D

24. C

25. C

26. D

27. C

28. B

29. A

30. D

31. B

32. C