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Henrico County Public Schools, Virginia
Algebra and Functions

Data Analysis

SOL Review Materials
The student will calculate probabilities. Key concepts include:
a)   conditional probability;
b)   dependent and independent events;
c)   addition and multiplication rules;
d)   counting techniques (permutations and combinations); and
e)   Law of Large Numbers.
Essential Knowledge and Skills 
  • Compare and contrast permutations and combinations.
  • Calculate the number of permutations of n objects taken r at a time.
  • Calculate the number of combinations of n objects taken r at a time.
  •  Define and give contextual examples of complementary, dependent, independent, and mutually exclusive events.
  • Given two or more events in a problem setting, determine if the events are complementary, dependent, independent, and/or mutually exclusive.
  • Find conditional probabilities for dependent, independent, and mutually exclusive events.
  • Represent and calculate probabilities using Venn diagrams and probability trees.
  • Analyze, interpret and make predictions based on theoretical probability within real-world context.
  • Given a real-world situation, determine when to use permutations or combinations.
Essential Understandings
  • The Fundamental Counting Principle states that if one decision can be made n ways and another can be made m ways, then the two decisions can be made nm ways.
  • Permutations are used to calculate the number of possible arrangements of objects.
  • Combinations are used to calculate the number of possible selections of objects without regard to the order selected.
  • A sample space is the set of all possible outcomes of a random experiment.
  • An event is a subset of the sample space.
  • P(E) is a way to represent the probability that the event E occurs.
  • Mutually exclusive events are events that cannot both occur simultaneously.
  • If A and B are mutually exclusive then P(A U B) = P(A) + P(B).
  • The complement of event A consists of all outcomes in which event A does not occur.
  • P(B|A) is the probability that B will occur given that A has already occurred.  P(B|A) is called the conditional probability of B given A.
  • Venn diagrams may be used to examine conditional probabilities (See chart in Curriculum Framework)..
  • Two events, A and B, are independent if the occurrence of one does not affect the probability of the occurrence of the other. If A and B are not independent, then they are said to be dependent. 
  • If A and B are independent events, then P(A intersection B)=P(A)P(B)
  • The Law of Large Numbers states that as a procedure is repeated again and again, the relative frequency probability of an event tends to approach the actual probability.
Vertical Articulation
  • SOL 7.9 - investigate/describe the difference between experimental/theoretical probability.
  • SOL 8.12 - determine the probability of indep/dep events with and without replacement.
  • SOL AII.12 - compute/distinguish between permutation/combination and apply.
Instructional Materials
  1. AFDA.6a - Notes: Conditional Probability (ppt)
  2. AFDA.6b - Notes: Dependent and Independent Events (ppt)
  3. AFDA.6c - Notes: Addition and Multiplication Rules (ppt)
  4. AFDA.6d - Notes: Counting Techniques (ppt)
  5. AFDA.6e - Notes: Law of Large Number (ppt)
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