VI. Statistical Reasoning

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A. Counting principles

1. Determine the nature and the number of elements in a finite sample space.

a. Make lists, tables, and tree diagrams to represent all possible outcomes in determining specifics of the sample space.
b. Determine the number of ways an event may occur using combination and permutation formulas and the Fundamental Counting Principle.

B. Computation and interpretation of probabilities

1. Compute and interpret the probability of an event and its complement.

a. Conduct an experiment or simulation to compute the empirical probability of an event and its complement.
b. Compute and interpret the theoretical probability of a simple event and its complement.
c. Compare the empirical and theoretical probabilities of an event (e.g., experimental probabilities converge to theoretical probability as the number of trials increases).

2. Compute and interpret the probability of conditional and compound events.

a. Distinguish between independent and dependent events.
b. Explain the meaning of conditional probability and know when to use it.
c. Compute conditional probability.
d. Compute the probability of compound events using tree diagrams, tables, and other methods.
e. Compute the probability for dependent or independent compound events.