Statistics and Risk
Management
Basic Probability
Video URL:
http:// jukebox.esc13.net/untdeveloper/Videos/Basic%20Probability.mov
Vocabulary List:
Probability: the study of random event denoting the relative frequency of
occurrence when repeating the process
Frequentists: Those who consider probability to be the relative frequency "in
the long run" of outcomes
Bayes’ Theorem: Thomas Bayes’ methodology on how to accumulate
information and revise estimates of Probability
Odds: the ratio of the probability of an event happening to the probability of it
not happening.
Analytical Method: the process of calculating a statistical problem.
Events: any set of outcomes of an experiment.
Independent Events: occur when there is no cause or effect relationship
between two events.
Mutually Exclusive Events: two events that cannot occur together.
Exhaustive Events: all possible occurrences of the events exist in the set of
outcomes.
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Resources:
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
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_probabilit
y.htm
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Basic Probability Practice 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 question or set of questions designed to collect data about a specific group of people 2.__________A variety of outcomes that are equally likely to occur 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 diagram used to show the total number of possible outcomes in a probability experiment 8.__________A randomly‐selected group that is used to represent a whole population 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. What is the probability of choosing the letter i from the word probability? 12. What is the probability of choosing an ace from a standard deck of playing cards? 13. What is the probability of getting a 0 after rolling a single die numbered 1 to 6? 14. What is the probability of drawing a shell button if there are 5 white buttons, 4 shell buttons, and 3 black buttons? Copyright © Texas Education Agency, 2012. All rights reserved.
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Basic Probability Practice Test
Name:_____________________
A.
B.
C.
D.
Experiment Outcome Event Probability 15.__________The result of a single trial of an experiment 16.__________One or more outcomes of an experiment 17.__________The measure of how likely an event is 18.__________A situation involving chance or probability that leads to results called outcomes 19. 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 20. Which of the following is an outcome? A.
B.
C.
D.
Rolling a pair of dice Landing on red Choosing 2 marbles from a jar None of the above. Copyright © Texas Education Agency, 2012. All rights reserved.
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Basic Probability Practice Test KEY
1. B
2. F
3. E
4. D
5. C
6. I
7. G
8. H
9. A
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
6/15 = 2/5
1/9
4/52 = 1/13
0/6
4/12 = 1/3
B
C
D
A
D
B
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Student Assignment
4.1a Basic Probability Introduction
Name:_____________________
You need to call your Father while he is at work today. He will works 8
hours, but 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)=
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 of 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)=
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Student Assignment
4.2a Basic Probability Rules
Name:_____________________
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)=
Explain how you figured out the probability.
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Student Assignment
4.3a Basic Probability Bayes’ Theorem
Name:_____________________
A doctor is called to see a sick child. The doctor has prior information that 90% of
sick children in that neighborhood have the flu, while the other 10% are sick with
measles.
Let “F” stand for an event of a child being sick with FLU and “M” stand for an event
of a child being sick with MEASLES. Assume for simplicity that F∪ M = Ω, i.e., that
there no other maladies in that neighborhood.
Before seeing the child the doctor figures the probability is .90 that the child will
have the FLU or .10 that the child while have the MEASLES.
A well-known symptom of MEASLES is a rash (the event of having which we
denote R). P(R|M) = .95. However, occasionally children with FLU also develop
rash, so that P(R|F) = 0.08.
Upon examining the child, the doctor finds a rash. He still believes it is the FLU
and not the MEASLES. What does a probability calculation say about the child
having measles with the rash? Is the Doctor correct in his diagnosis?
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Use this formula and plug in the
probabilities.
Is the doctor correct in thinking it is the flu? (YES) or (NO)
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Explore Activity:
Definition of Probability – Flip a coin 20 times and record the sequence of
heads and tails in a table:
Toss
H or T
Cumulative
Freq of H
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Then calculate the cumulative frequency of heads (number of heads so far
divided by number of tosses). For example, if your first 5 tosses were
HHTHT, then your table would start out looking like this:
Toss
1
H or T
H
Cumulative 1/1 = 1
Freq of H
2
H
2/2 = 1
3
T
2/3 =
0.67
4
H
2/4 =
0.50
5
T
3/5 =
0.60
After you calculate the cumulative frequencies, on a graph like the one
below, draw a horizontal line across the graph at a cumulative frequency of
0.5 (Why? What does this represent?). Then plot your cumulative
frequencies as ordered pairs (Toss, Cumulative freq) and connect these
points creating a ‘zigzag’ effect.
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Cumulative Freq of H
1
0.8
0.6
0.4
0.2
2
4
6
8
10
12
14
16
18
Tosses
20
Compare your graph to the graphs made by others in your class (or, if you
are working at home, repeat the 20 coin tosses and make a new graph as
many times as you can stand it!). You will probably see quite a bit of
variation among graphs, particularly for the first several coin tosses. At what
cumulative frequency do most of the graphs come close to? Theoretically,
what should be the cumulative frequency of heads? Why might the result of
20 coin tosses not quite match the theoretical outcome? What do you think
you would see if you doubled the number of coin tosses?
Repeat this activity with something other than a coin (a plastic bottle cap or
a spoon for example). Find something that if tossed will land in one of two
ways – up or down (of course, you will have to decide which way is up!).
What do you think will happen after 20 tosses? Should the cumulative
frequency of ‘up’ be 0.50 like it was for coins? After you complete the
tosses, plot the points first and then determine where a horizontal line
should be drawn to represent the theoretical probability. Your graph should
look something like the one for the coins, but the horizontal line will possibly
be located somewhere other than at 0.50. This illustrates the idea that in the
long run, the frequency of outcomes approaches the theoretical probability
of that outcome.
Video Links – Check out the relevant links at Khan Academy for more
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information andCopyright
examples:
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