Capital Area Career Center
Lesson Plan 9 – Probabilities in AutoTech
Content Standard (s): What relevant goals will this design address?
S4.2.1, S4.2.2
Stage 1: Desired Results
What are the “big ideas”? What specific understandings about them are desired?
What misunderstandings are predictable?
Students will understand:
 Tree Diagrams
 Venn Diagrams
Essential Question(s): What arguable, recurring, and thought-provoking questions will
guide inquiry and point toward the big ideas of the unit?
What is the best way to determine probabilities?
Knowledge & Skill
 What is the key knowledge and skill needed to develop the desired
understandings? Students will know …
Determining the correct sample space, formula awareness and usage, etc.
 What knowledge and skill relates to the content standards on which the unit is
focused? Students will be able to…
Apply probability concepts to practical settings.
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Stage 2: Assessment Evidence
What evidence will be collected to determine whether or not the understandings have
been developed, the knowledge and skill attained, and the state standards met?
[Anchor the work in performance tasks that involve application, supplemented as
needed by prompted work, quizzes, observations, etc.]
Performance Task Summary:
Summary in G.R.A.S.P.S. form
Rubric Titles (Key Criteria)
Probability: Type
Students will collect data related to a realworld situation, calculate probabilities for
multi-event situations, and prepare a report
to an audience appropriate for the situation.
Usage: Appropriate for the situation.
Probability calculated
Formative Assessment
Summative Assessment
Presentation, Authentic, Program
Contextual
End of Unit/Course, Standardized, CACCwide
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Stage 3: Learning Activities
What sequence of learning activities and teaching will enable students to perform well
at the understandings in Stage 2 and thus display evidence of the desired results in
stage one? Learning Activities: Consider the W.H.E.R.E.T.O elements:
Tree diagrams
Tree diagrams allow us to see all possible outcomes of an event and calculate their
probabilities. Each branch in a tree diagram represents a possible outcome for an
event.
If two events are independent, then the outcome of one has no effect on the
outcome of the other. For example, if we toss two coins, getting a head with the
first coin will not affect the probability of getting a head with the second coin.
Example 1
Three coins are tossed. What is the probability of getting:
1. three heads?
2. two heads and a tail?
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The Answer
From the tree diagram we can see that there are eight possible outcomes. To find
out the probability of a particular outcome we need to look at all the available
paths (set of branches) in the tree diagram.
1. Only one path has three heads, so the probability of getting three heads is:
Another way to look at it is by multiplying the individual probabilities:
1 1 1 1
x x 
or .5 x .5 x. 5 = .125
2 2 2 8
2. Three of the outcomes show two heads and a tail, so the probability of getting
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two heads and a tail is:
or 3 x (.5 x .5 x.5) = .375
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Example 2
At the Ingham County Health Department, 58% of the clients are female, 23% are
low or non-English speakers, and 69% are of child-bearing age.
1. If an average of 743 clients have appointments each week at the Health
Department, how many are female, low or non-English speakers of child-bearing
age?
743 x .58 x .23 x .69 = 68 clients
2. Why is this important for the Ingham County Health Department to know?
Venn Diagrams
A Venn diagram is a drawing, in which circular areas represent groups of
items sharing common properties. The drawing consists of two or more
circles, each representing a specific group. This process of visualizing
logical relationships was devised by John Venn (1834-1923).
Each Venn diagram
begins with a
rectangle representing
the universal set.
Then each set in the
problem is
represented by a
circle. Any values that
belong to more than
one set will be placed
in the sections where
the circles overlap.
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The Venn diagram at the left
shows two sets A and B. Values
that belong to both set A and
set B are located in the center
region labeled A ^ B where the
circles overlap.
The notation A v B represents the entire region
covered by both sets A and B.
If we cut out sets A and B, the remaining region in U
would be labeled ~(A v B).
** The most interesting features of Venn
diagrams are the areas or sections where the
circles overlap one another -- implying that a
sharing is occurring.
Example 3
During a 6 month time period
in the AutoTech Program at
CACC, a total of 350 cars had
general service appointments.
This information is shown in
the Venn Diagram below:
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Oil
Changes
125
18
38
6
87
27
Tire
Balance
48
Coolant
Flush
1. How many vehicles were serviced for only a coolant flush and a tire balance?
2. How many vehicles were serviced for a coolant flush or a tire balance?
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3. How many vehicles were serviced for one service only?
4. How many vehicles were serviced for all three services?
5. How many vehicles did not have any of the 3 services?
6. Why would this be important for a service center to know?
GLOSSARY OF TERMS
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G.R.A.S.P.S. form for performance task:
Goal
Role
Audience
Situation
Product/Performance/Purpose
Standards & Criteria for Success
Consider the W.H.E.R.E.T.O. elements for structuring learning activities:
Where – Help the students know where the unit is going and what is expected. Help the
teacher know where the students are coming from (prior knowledge, interests).
Hook – Hook all students and hold their interest.
Equip – Equip students, help them experience the key ideas, and explore the issues.
Provide – Provide opportunities to rethink and revise their understanding and work.
Evaluate – Allow students to evaluate their work and its implications.
Tailored – Tailored (personalized) to the different needs, interests, abilities of learners.
Organized – Organized to maximize initial and sustained engagement as well as effective
learning.
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