The How Random Is My Life? Project addresses the followingin High School Geometry.
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.
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 terms of the model.
Use probabilities to make fair decisions (e.g. drawing by lots, using a random number generator).
Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
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”).
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 characteristic to determine if they are independent.
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 sample space to decide if events are independent and to approximate conditional probabilities.
Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in the form of a model.
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.