(P) Probability Learners will understand and apply basic concepts of probability.

MAT-10.DPS.05 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”).

MAT-07.DPS.P.01 Develop a probability model to find probabilities of theoretical events and contrast probabilities from an experimental model.

MAT-07.DPS.P.02 Develop a probability model to find theoretical probabilities of independent compound events.

MAT-10.DPS.05Describe 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").

MAT-10.DPS.06 Recognize that event A is independent of event B if the probability of event A does not change in response to the occurrence of event B. Apply the formula P(A and B) = P(A)·P(B) given that events A and B are independent.

MAT-10.DPS.07 Recognize the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred. Calculate the conditional probability of A given B and interpret
the answer in context.

MAT-10.DPS.08 Apply the formula P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in context.

MAT-10.DPS.09 Determine the number of outcomes using permutations and combinations in context.

MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.

MAT-12.DPS.10 Determine when the order in counting matters and use permutations and combinations to compute probabilities of events accordingly. Determine probability situations as conditional, "or" (union), or "and" (intersection),
and determine the probability of an event.

MAT-12.DPS.11 Use permutations and combinations to compute probabilities of compound events and solve problems.

MAT-12.DPS.12 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.

MAT-12.DPS.13 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

MAT-12.DPS.14 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

MAT-12.DPS.15 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.

MAT-12.DPS.16 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.

MAT-12.DPS.17 Use probabilities to make fair decisions.

MAT-12.DPS.18 Analyze decisions and strategies using probability concepts.