Number of Cases (Counting Principle)

  1. Event: The outcome of an experiment or observation that can be repeated under the same conditions.
  2. 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 .

Number of Cases Where Event or Event Occurs

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)

Number of Cases Where Event and Event Occur Simultaneously

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)