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Henrico County Public Schools, Virginia
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 Algebra and Functions Data Analysis SOL Review Materials Frequently Asked Questions
The student will calculate probabilities. Key concepts include:
a)   conditional probability;
b)   dependent and independent events;
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.
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