Conditional Probability and the Rules of Probability
|Understand independence and conditional probability and use them to interpret data. [Link to data from simulations
|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. 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.
|5. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday
|Use the rules of probability to compute probabilities of compound events in a uniform probability model.|
|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.
|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.|
|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.
|9. (+) Use permutations and combinations to compute probabilities of compound events and solve problems.|