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[MATHEMATICS: PROBABILITY] December 14, 2007
Probability
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[MATHEMATICS: PROBABILITY] December 14, 2007
Probability Summary
Strand
Data Analysis, Statistics,
and Probability
Total
Standard
14
Topic
Probability
Number of
Elements
8
8
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[MATHEMATICS: PROBABILITY] December 14, 2007
Topic/Course: Probability
Strand: Data Analysis, Statistics, and Probability
Standard 14: PROBABILITY: Understand and apply basic notions of chance and
probability.
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught, such as:
 Implement an experiment and figure out the probabilities involved.
Level 3.5
Level 3.0
While engaged in tasks involving probability the student will:
 Describe the relationship among events (inclusive, disjoint, complimentary,
independent, dependent) (e.g., provide an example of inclusive, disjoint,
complimentary, independent events, and dependent events). MA.P.14.1
 Calculate the probability of two events under union and intersection (e.g.,
determine the probability of two events that are intersections and two events
that are unions). MA.P.14.2
 Calculate the probability of an outcome for an experiment with and without
replacement (e.g., show/explain how to find the probability of events occurring
with and without replacement). MA.P.14.5
 Apply discrete random variables to solve for the probability of experimental
outcomes (e.g., show/explain how to apply discrete random variables to solve
for probability of experimental outcomes. i.e., determine the probability of
rolling three 4’s in nine rolls of a number cube). MA.P.14.6
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 recognizes or recalls specific terminology such as:
o
 recognizing and recalling the accuracy of basic solutions and information such
as:
o Recognize the relationship among events.
o Recognize the probability of two events under union and
intersection.
o Recognize experiments with and without replacement.
o Recognize discrete random variables can be applied to solve for
probability of experimental outcomes.
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
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[MATHEMATICS: PROBABILITY] December 14, 2007
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0

Level 3.0

Level 2.0
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[MATHEMATICS: PROBABILITY] December 14, 2007
Topic/Course: Probability
Strand: Data Analysis, Statistics, and Probability
Standard 14: PROBABILITY: Understand and apply basic notions of chance and
probability.
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught, such as:
 Differentiate between using permutations and combinations.
 Differentiate between Independent and Dependent Events.
Level 3.5
Level 3.0
While engaged in tasks involving probability the student will:
 Differentiate between theoretical and experimental probability (e.g., compare
the theoretical probability to the experimental probability of an experiment
and analyze the difference between them). MA.P.14.3
 Explain the difference between probability and odds and convert from one to
the other (e.g., express the change of an event occurring as a probability and
as odds, and describe how the representations reflect the events). MA.P.14.4
 Estimate and calculate expected values (e.g., show/explain how to calculate
the expected values of an experiment). MA.P.14.7
 Apply permutations, combinations, and the fundamental counting principle to
calculate the probability of two events (e.g., use permutations (or
combinations) to determine the total number of possible outcomes and the
total number of intended outcomes, and then represents the values as a ratio
and simplifies). MA.P.14.8
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 recognizes or recalls specific terminology such as:
o
 recognizing and recalling the accuracy of basic solutions and information such
as:
o Recognize experimental and theoretical probability.
o Recognize probability and odds.
o Recognize expected values.
o Recognize permutations, combinations, and the fundamental
counting principle.
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
5
[MATHEMATICS: PROBABILITY] December 14, 2007
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0

Level 3.0

Level 2.0

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