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 realworld context.
 Given a realworld 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(BA) is the probability that B will occur given that A has already occurred. P(BA) 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 
 AFDA.6a  Notes: Conditional Probability (ppt)
 AFDA.6b  Notes: Dependent and Independent Events (ppt)
 AFDA.6c  Notes: Addition and Multiplication Rules (ppt)
 AFDA.6d  Notes: Counting Techniques (ppt)
 AFDA.6e  Notes: Law of Large Number (ppt)

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