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### IC Making Inferences and Justifying Conclusions

- IC.1.S Make inferences and justify conclusions from sample surveys, experiments, and observational studies
- IC.1.S.1 Use data from a sample survey to estimate a population mean or proportion. Develop a margin of error through the use of simulation models for random sampling.
- IC.1.S.2 Use data from a randomized experiment to compare two treatments. Use simulations to decide if differences between parameters are significant.

### CP Conditional Probability and the Rules of Probability

- CP.2.S Understand independence and conditional probability and use them to interpret data
- CP.2.S.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”).
- CP.2.S.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. - CP.2.S.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. - CP.2.S.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.
- CP.2.S.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

- CP.3.S Use the rules of probability to compute probabilities of compound events
- CP.3.S.1 Find the conditional probability of
*A*given*B*. - CP.3.S.2 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. - CP.3.S.3 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. - CP.3.S.4 Use permutations and combinations to compute probabilities of compound events and solve problems.
- CP.3.S.5 Use visual representations in counting (e.g. combinations, permutations, etc.) including but not limited to: Venn Diagrams, Tree Diagrams.

- CP.3.S.1 Find the conditional probability of

### MD Using Probability to Make Decisions

- MD.4.S Calculate expected values and use them to solve problems
- MD.4.S.1 Define 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.
- MD.4.S.2 Calculate the expected value of a random variable. Interpret the expected value of a random variable as the mean of the probability distribution.
- MD.4.S.3 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated. Find the expected value.
- MD.4.S.4 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically. Find the expected value.

- MD.5.S Use probability to evaluate outcomes of decisions
- MD.5.S.1 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. Find the expected payoff for a game of chance. Evaluate and compare strategies on the basis of expected values.
- MD.5.S.2 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
- MD.5.S.3 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).