Download Unit 6

Accelerated GSE Pre-Calculus
Unit Six Information
Curriculum Map: Probability
Concept 1: Rules of Probability
Concept 2: Calculate & Use Expected Values
Concept 3: Use Probabilities to Make Decisions
Content from Frameworks: Probability
Unit Length: Approximately 25 days
20152016
TCSS – Accelerated GSE Pre-Calculus – Unit 6
Curriculum Map
Big Idea / Unit
Students will use calculate, interpret and use probabilities and expected values to make decisions.
Unit Essential Questions:
How do you calculate, apply
and interpret probabilities?
Prerequisites: As identified by the GSE Frameworks
Length of Unit
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Understand the basic nature of probability
Determine probabilities of simple and compound events
Understand the Fundamental Counting Principle
Organize and model simple situations involving probability
Concept 1
Rules of Probability
25 Days
Concept 2
Concept 3
Calculate & Use Expected Values
Use Probabilities to Make Decisions
GSE Standards
MGSE9-12.CP.8 (+) Apply the general
Multiplication Rule in a uniform probability
model, P(A and B)=[P(A)] x [P(B│A)] =
[P(B)] x [P(A│B)], and interpret the answer
in terms of the model.
MGSE9-12.S.CP.9 (+) Use permutations and
combinations to compute probabilities of
compound events and solve problems.
GSE Standards
GSE Standards
MGSE9-12.S.MD.1(+) Define a random variable
MGSE9-12.S.MD.5(+) Weigh the possible
for a quantity of interest by assigning a numerical
outcomes of a decision by assigning probabilities
value to each event in a sample space; graph the
to payoff values and finding expected values.
corresponding probability distribution using the
MGSE9-12.S.MD.5a(+) Find the expected
same graphical displays as for data distributions.
payoff for a game of chance
MGSE9-12.S.MD.2(+) Calculate the expected
MGSE9-12.S.MD.5b(+) Evaluate and compare
value of a random variable; interpret it as the mean
strategies on the basis of expected values
of a probability distribution.
MGSE9-12.S.MD.6(+) Use probabilities to make
MGSE9-12.S.MD.3(+) Develop a probability
fair decisions (e.g., drawing by lots, using a
distribution for a random variable defined for a
random number generator).
sample space in which theoretical probabilities can
MGSE9-12.S.MD.7(+) Analyze decisions and
be calculated; find the expected value
strategies using probability concepts (e.g., product
MGSE9-12.S.MD.4(+) Develop a probability
testing, medical testing, pulling a hockey goalie at
distribution for a random variable defined for a
the end of a game).
sample space in which probabilities are assigned
empirically; find the expected value
Supporting Standards
MGSE7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
MGSE9-12.S.CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their
probabilities, and use this characterization to determine if they are independent.
MGSE9-12.S.CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the
conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
MGSE9-12.S.CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms
of the model.
MGSE9-12.S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
TCSS
7/27/2015
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TCSS – Accelerated GSE Pre-Calculus – Unit 6
Lesson Essential Question
How do I use the General Multiplication
Rule to calculate probabilities?
How do I determine when to use a
permutation or a combination to calculate a
probability?
Vocabulary
General Multiplication Rule
Conditional Probability
Combinations
Permutations
Resources – Concept 1
 Combinations and
Permutations Overview with
Practice
 Combination calculator
activity
These tasks were taken from the
GSE Frameworks.
 Permutations and
Combinations Task
 Testing Learning Task
Differentiated Activities
Concept 1

TCSS
Lesson Essential Question
How do I identify a random variable?
How do I graphically display the probability
distribution of a random variable?
How do I calculate the expected value of a
random variable?
How do I calculate theoretical and empirical
probabilities of probability distributions?
How do I represent and calculate payoff values
in a game of chance?
How do I use expected values to make
decisions?
How do I explain the decisions I make using
expected values?
Vocabulary
Random Variable
Expected Value
Sample Space
Theoretical Probabilities
Empirical Probabilities
Vocabulary
Pay off
Odds
Resources – Concept 2
 Discrete Random Variables
 Expected Value Practice
 Expected Value Worksheet
These tasks were taken from the
GSE Frameworks.
 Please Be Discrete Task
Resources – Concept 3
 Statistics Review
These tasks were taken from the
GSE Frameworks.
 Lottery Learning Task
 Mega Millions Practice Task
 Design a Lottery game Project
Differentiated Activities
Concept 2
Medical Testing FAL
Differentiated Activities
Concept 3

7/27/2015
Representing Conditional
Probabilities 2 FAL
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TCSS – Accelerated GSE Pre-Calculus – Unit 6
Unit 6 Checklist – Probability
Good luck to ________________________Date_______ Period___
Keep this list handy and refer to it periodically to see how you are doing. If you know how to each of these you should do well on
an exam.
In this unit I :
sort of
really
can calculate probabilities using the general Multiplication Rule in a probability model.
can use permutations and combinations to calculate probabilities of compound events
and to solve problems.
given a probability situation, theoretical or empirical, understand how to define a
random variable, assign probabilities to its sample space, and graph the probability
distribution of the random variable.
can calculate the expected value of a random variable
can develop a theoretical and empirical probability distribution and find the expected
value.
can develop a probability distribution for a random variable representing payoff
values in a game of chance.
can make and explain decisions based on expected values.
TCSS
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