Statistics and Probability

Use simulation to determine whether the experimental probability generated by sample data is consistent with the theoretical probability based on known information about the population.

Describe events as subsets of the outcomes in a sample space using characteristics of the outcomes or as unions, intersections and complements of other events.

Develop and understand independence and conditional probability.

Use a 2-way table to develop understanding of the conditional probability of A given B (written P(A|B)) as the likelihood that A will occur given that B has occurred. That is, P(A|B) is the fraction of event B’s outcomes that also belong to event A.

Understand that event A is independent from event B if the probability of event A does not change in response to the occurrence of event B. That is P(A|B)=P(A).

Represent data on two categorical variables by constructing a two-way frequency table of data. Interpret the two-way table as a sample space to calculate conditional, joint and marginal probabilities. Use the table to decide if events are independent.

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

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 context.

Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in context.

Apply the general Multiplication Rule P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in context. Include the case where A and B are independent: P(A and B) = P(A) P(B).