S-CP.A.5  Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.   Modeling Standard

Embed with S-CP.A.5, S-CP.A.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”).  Modeling Standard

Embed with S-CP.A.5, S-CP.A.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.  Modeling Standard

Embed with S-CP.A.5, S-CP.A.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.  Modeling Standard

S-CP.A.6  Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.   Modeling Standard

S-CP.A.7  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.   Modeling Standard

S-CP.A.8  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.    Modeling Standard

Achievement Level Descriptors

Assessment Targets (incorporate as many as possible) & Evidence

Embed with S-CP.A.5, S-CP.A.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”).  Modeling Standard

Embed with S-CP.A.5, S-CP.A.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.  Modeling Standard

Embed with S-CP.A.5, S-CP.A.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.  Modeling Standard

S-CP.A.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. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.  Modeling Standard

S-CP.B.9. Use permutations and combinations to compute probabilities of compound events and solve problems.  Modeling Standard

S-MD.B.6. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).  Modeling Standard

S-MD.B.7. Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).  Modeling Standard