Probability - Survey of Mathematics Textbook - Pearson

SEVENTH EDITION and EXPANDED SEVENTH EDITION Probability  The Nature of Probability Experimental vs. Theoretical  An experiment is a controlled operation that yields a set of results.  The possible results of an experiment are called its outcomes.  An event is a subcollection of the outc...

SEVENTH EDITION and EXPANDED SEVENTH EDITION Probability  The Nature of Probability Experimental vs. Theoretical  An experiment is a controlled operation that yields a set of results.  The possible results of an experiment are called its outcomes.  An event is a subcollection of the outcomes of an experiment.  Empirical/Experimental probability is the relative frequency of occurrence of an event and is determined by actual observations of an experiment.  Theoretical probability is determined through a study of the possible outcome that can occur for the given experiment.  number of times event E has occurred P (E )  total number of times the experiment has been performed  Example: In 100 tosses of a fair die, 19 landed showing a 3. Find the experimental probability of the die landing showing a 3.  Let E be the event of the die landing showing a 3. 19 P (3)  0.19 100  The law of large numbers states that probability statements apply in practice to a large number of trials, not to a single trial. It is the relative frequency over the long run that is accurately predictable, not individual events or precise totals.