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.
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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…
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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
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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
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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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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.
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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
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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
Use presentation and
BasicProbability_Rules.pptx
Provided .docx files
4.2a
BasicProbabiltiy_Rules.docx
Use presentation and
BasicProbability_Bayes.pptx
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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%
Use presentation and
BasicProbability_Bayes.pptx
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)
Provided .docx files
4.3a
BasicProbability_Bayes.docx
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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.
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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
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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.
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Student Assignment
4.3a Basic Probability Bayes’ Theorem
ANSWER:
= .95 x .10 / (.95
= .095 / .095 + .072
x .10) + ( .08 x .90)
= .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.
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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?
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Basic Probability Test
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?” ________
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Basic Probability Test
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
d. None of the above
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
d. None of the above
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
d. None of the above
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%
d. None of the above
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.
b.
c.
d.
3/100
9/2500
1/330
None of the above
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Basic Probability Test
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.
B.
C.
D.
Toss a coin
Choose a number at random from 1-8
Choose a letter at random from the word SCHOOL
None of the above
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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
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