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Number of Cases (Counting Principle)

Event: The outcome of an experiment or observation that can be repeated under the same conditions.
Number of Cases: The total number of possible outcomes for an event.

For example, when rolling a single die, the event “rolling an even number” is an event. The outcomes that satisfy this event are

, and

. Thus, the number of cases is

In general, if event

and event

cannot occur simultaneously, and the number of cases where

occurs is

, and the number of cases where

occurs is

, then:

(Number of cases where or occurs)

In general, if the number of cases where event

occurs is

, and for each case of

, there are

cases where event

occurs, then:

(Number of cases where and occur simultaneously)