| dbo:abstract
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- In probability theory and logic, a set of events is jointly or collectively exhaustive if at least one of the events must occur. For example, when rolling a six-sided die, the events 1, 2, 3, 4, 5, and 6 balls of a single outcome are collectively exhaustive, because they encompass the entire range of possible outcomes. Another way to describe collectively exhaustive events is that their union must cover all the events within the entire sample space. For example, events A and B are said to be collectively exhaustive if where S is the sample space. Compare this to the concept of a set of mutually exclusive events. In such a set no more than one event can occur at a given time. (In some forms of mutual exclusion only one event can ever occur.) The set of all possible die rolls is both mutually exclusive and collectively exhaustive (i.e., "MECE"). The events 1 and 6 are mutually exclusive but not collectively exhaustive. The events "even" (2,4 or 6) and "not-6" (1,2,3,4, or 5) are also collectively exhaustive but not mutually exclusive. In some forms of mutual exclusion only one event can ever occur, whether collectively exhaustive or not. For example, tossing a particular biscuit for a group of several dogs cannot be repeated, no matter which dog snaps it up. One example of an event that is both collectively exhaustive and mutually exclusive is tossing a coin. The outcome must be either heads or tails, or p (heads or tails) = 1, so the outcomes are collectively exhaustive. When heads occurs, tails can't occur, or p (heads and tails) = 0, so the outcomes are also mutually exclusive. (en)
- По́лной гру́ппой (системой) собы́тий в теории вероятностей называется система случайных событий такая, что в результате произведённого случайного эксперимента непременно произойдет одно и только одно из них.. (ru)
- 互補事件，互餘事件、不遺漏事件、周延事件，在概率論和邏輯學中指的是一個包含所有可能發生的事件的事件集合。 例如，當一個投擲一個 六面骰子時，由投出1、投出2、投出3、投出4、投出5、投出6所構成的集合是不遺漏的，因為它们涵蓋了所有可能的结果。 另一種描述不遺漏的方法是，事件的集合的并集必須包括整个樣本空間中的所有可能發生的事件。例如，如果事件A和事件B是不遺漏的，那麼他們滿足： S指樣本空間。 互補事件的一個特別例子是互補且互斥的事件。在一個互斥的集合中，一次只能發生一个事件，比如說擲骰子不可能同時擲出兩個數字。 (zh)
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| rdfs:comment
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- По́лной гру́ппой (системой) собы́тий в теории вероятностей называется система случайных событий такая, что в результате произведённого случайного эксперимента непременно произойдет одно и только одно из них.. (ru)
- 互補事件，互餘事件、不遺漏事件、周延事件，在概率論和邏輯學中指的是一個包含所有可能發生的事件的事件集合。 例如，當一個投擲一個 六面骰子時，由投出1、投出2、投出3、投出4、投出5、投出6所構成的集合是不遺漏的，因為它们涵蓋了所有可能的结果。 另一種描述不遺漏的方法是，事件的集合的并集必須包括整个樣本空間中的所有可能發生的事件。例如，如果事件A和事件B是不遺漏的，那麼他們滿足： S指樣本空間。 互補事件的一個特別例子是互補且互斥的事件。在一個互斥的集合中，一次只能發生一个事件，比如說擲骰子不可能同時擲出兩個數字。 (zh)
- In probability theory and logic, a set of events is jointly or collectively exhaustive if at least one of the events must occur. For example, when rolling a six-sided die, the events 1, 2, 3, 4, 5, and 6 balls of a single outcome are collectively exhaustive, because they encompass the entire range of possible outcomes. Another way to describe collectively exhaustive events is that their union must cover all the events within the entire sample space. For example, events A and B are said to be collectively exhaustive if where S is the sample space. (en)
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