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 andb are independent if the probability of A andb 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 givenb as P(A and B)/P(B), and interpret independence of A andb as saying that the conditional probability of A givenb is the same as the probability of A, and the conditional probability ofb 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.3.S.5 Use visual representations in counting (e.g. combinations, permutations, etc.) including but not limited to: Venn Diagrams, Tree Diagrams.
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.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.