LAC 28:CXLII.2313. Statistics and Probability Conditional Probability and the Rules of Probability

A. Understand independence and conditional probability and use them to interpret data. 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”. 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. 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. 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. 5. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. B. Use the rules of probability to compute probabilities of compound events in a uniform probability model. 1. 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. 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.