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UNIT 3: Probability (4 weeks) GHS Department of Matheπ πatics Int. Math 3: Probability (4 weeks) I Can . . . • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • I can define event and sample space. I can establish events as subsets of a sample space. I can define union, intersection, and complement. I can establish events as subsets of a sample space based on the union, intersection, and/or complement of other events. I can define and identify independent events and justify my conclusions. I can explain and provide an example to illustrate that for two independent events, the probability of the events occurring together is the product of the probability of each event. I can calculate the probability of an event. I can predict if two events are independent, explain my reasoning, and check my statement by calculating P(A and B) and P(A) x P(B). I can define dependent events and conditional probability. I can explain that conditional probability is the probability of an event occurring given the occurrence of some other event and give examples that illustrate conditional probability. I can explain that for two events A and B, the probability of event A occurring given the occurrence of and give examples to show how to use the formula. event B is I can explain that A and B are independent events if the occurrence of A does not impact the probability of B occurring and vice versa. I can determine when a two-way frequency table is an appropriate display for a set of data. I can collect data from a random sample. I can construct a two way frequency table. I can pose a question for which a two-way frequency is appropriate, use statistical techniques to sample the population, and design an appropriate product to summarize the process and report the results. I can illustrate the concept of conditional probability and independence using everyday examples of dependent and independent events respectively. I can apply the fundamental counting principle to find the total number of possible outcomes in a sample space. I can define factorial, permutation, combination, and compound event. I can distinguish between situations that require permutations and those that require combinations. I can apply the permutation formula and the combination formula. I can compute probabilities of an event. I can write and solve original problems involving compound events, permutations, and/or combinations. I can use probability to create a method for making a fair decision. I can use probability to analyze the results of a process and decide if it resulted in a fair decision. I can analyze data to determine whether or not the best decision was made. I can define population and population parameter. I can explain why randomization is used to draw a sample that represents a population well. I can recognize that statistics involves drawing conclusions about a population based on the results obtained from a random sample of the population. I can choose a probability model for a problem situation. I can conduct a simulation of the model and determine which results are typical of the model. Vocabulary • • • • • • • • • • • • • • • • • • • • • • • • • Event Sample space outcome Subset Union Intersection Complement Independent events Dependent events Probability Product event Conditional probability Two-way frequency table Display Data random sample fundamental counting principle. Factorial Permutation Combination Simulation Fair Theoretical probability Experimental probability model Common Core State Standards S.CP.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”) S.CP.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 this characterization to determine if they are independent. S.CP.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 S.CP.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. S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems S.MD.6 (+) Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). S.MD.7 (+) Use probability to evaluate outcomes of decisions. Analyze decisions and strategies using probability Integrated Math 3 – Unit 3 – Probability Page 2 • • concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game) S.IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population S.IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls head side up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model? Standards for Mathematics Practices Make sense of problems and persevere in solving problems. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Integrated Math 3 – Unit 3 – Probability Page 3