Читать книгу Probability and Statistical Inference - Robert Bartoszynski - Страница 29

Consider an experiment of tossing a coin three times, with the sample space consisting of outcomes described as HHH, HHT, and so on. Let and be the events “heads and tails alternate” and “heads on the last toss,” respectively. The event occurs if either heads or tails occur at least twice in a row so that , while is “tails on the last toss,” hence, . The union is the event “either the results alternate or it is heads on the last toss,” meaning . Observe that while has two outcomes and has four outcomes, their union has only five outcomes, since the outcome HTH appears in both events. This common part is the intersection .

Some formulas can be simplified by introducing the operation of the difference of two events.

Definition 1.3.7 The difference, of events and contains all sample points that belong to but not to

The symmetric difference, , contains sample points that belong to or to , but not to both of them: