The Nature of Probability

• An experiment is a controlled operation that yields a set of results.
• The possible results of an experiment are the outcomes
• An event is a subset of the outcomes of an experiment.
• Empirical Probability is found by conducting the experiment a number of times and counting the number of times an event occurs.
• P(E) = #of times E occurs/ # of times the experiment is conducted.
• The law of large numbers states that probability statements apply in practice to a large number of trials, not a single trial. It is the relative frequency over the long run that is accurately predictable, not individual events or precise totals.
• Do problems page 729 to 732.

Theoretical Probability

• Theoretical probability is found by studying the possible outcomes of an experiment.
• P(E) = # outcomes favorable to E/ # outcomes
• E can not occur if and only if P(E) = 0
• E must occur if and only if P(E) = 1
• 0 ≤ P(E) ≤ 1 by definition.
• The sum of all probabilities of the outcomes of an experiment is 1.
• P(A) + P(not A) = 1
• P(A) = 1-P(not A), P(not A) = 1-P(A)
• Do exercises 13 - 77 page 740