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UNIT 1: Probability
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Pacing: 4 weeks
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Stage 1 Desired Results
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Established Goals:
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CP.A.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
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CP.A.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 the characterization to determine if they are independent.
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CP.A.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.
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CP.A.4: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
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CP.A.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
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CP.B.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.
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CP.B.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.
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CP.B.8: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
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CP.B.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems.
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Transfer
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Students will be able to independently use their learning to….
- Apply concepts of probability to problems related to the real world (i.e. business, sports/gaming, etc).
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Meaning
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Understandings
Students will understand…
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Probability describes the likelihood an event will occur.
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The complement of event A consists of all outcomes in which event A does not occur.
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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.
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Events A and B are mutually exclusive if they cannot occur simultaneously.
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A probability is a number between 0 and 1 inclusively.
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Combinations and permutations can be used in the calculation of a statistical probability.
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How to calculate conditional probability.
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Essential Questions
Students will keep considering…
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Acquisition
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Students will know…
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The basic definition and rules of probability.
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The difference between odds and probability.
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How and when to apply the Addition Rule.
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How and when to apply the Multiplication Rule.
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How to use the Complement Rule to make calculating probabilities simpler.
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How to use combinations and permutations to calculate probabilities.
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Probabilities have a direct relationship to the gaming and sports industries.
- Probabilities are used to influence actions in various other industries such as manufacturing, construction and retail marketing.
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Students will be skilled at…
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Calculating simple probabilities, including complements of events.
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Calculating the odds in favor and against an event.
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Calculating conditional probabilities.
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Differentiating between independent and dependent events.
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Differentiating between mutually exclusive and overlapping events.
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Understanding and applying basic concepts of probability.
- Recognizing and calculating probabilities using combinations and permutations.
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