Probability

PS.P.1Understand and use the addition rule to calculate probabilities for mutually exclusive and nonmutually exclusive events.PS.P.10Describe 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.PS.P.2Understand and use 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.P.3Understand the multiplication counting principle, permutations, and combinations; use them to solve real-world problems. Use simulations with and without technology to solve counting and probability problems.PS.P.4Calculate the probabilities of complementary events.PS.P.5Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.PS.P.6Analyze decisions and strategies using probability concepts. Analyze probabilities to interpret odds and risk of events.PS.P.7Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.PS.P.8Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; Compute and interpret the expected value of random variables.PS.P.9Derive the binomial theorem by combinatorics. Use combinatorial reasoning to solve problems.
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