Conditional Probability and Rules of Probability

PS.SPCR.1Describe events as subsets of a sample space andPS.SPCR.1aUse Venn diagrams to represent intersections, unions, and complements.PS.SPCR.1bRelate intersections, unions, and complements to the words and, or, and not.PS.SPCR.1cRepresent sample spaces for compound events using Venn diagrams.PS.SPCR.2Use the multiplication rule to calculate probabilities for independent and dependent events. 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 this characterization to determine if they are independent.PS.SPCR.3Understand 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.PS.SPCR.4Construct 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.PS.SPCR.5Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.PS.SPCR.6Calculate the conditional probability of an event A given event B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.PS.SPCR.7Apply the Addition Rule and the Multiplication Rule to determine probabilities, including conditional probabilities, and interpret the results in terms of the probability model.PS.SPCR.8Use permutations and combinations to solve mathematical and real-world problems, including determining probabilities of compound events. Justify the results.
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