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互补事件.
互补事件,互余事件、不遗漏事件、周延事件,在概率论和逻辑学中指的是一个包含所有可能发生的事件的事件集合。 例如,当一个投掷一个 六面骰子时,由投出1、投出2、投出3、投出4、投出5、投出6所构成的集合是不遗漏的,因为它们涵盖了所有可能的结果。
另一种描述不遗漏的方法是,事件的集合的并集必须包括整个样本空间中的所有可能发生的事件。例如,如果事件A和事件B是不遗漏的,那么他们满足:
![{\displaystyle A\cup B=S}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8afcbe435af3dd55a609b01902cbffc04aee4fb0)
S指样本空间。
互补事件的一个特别例子是互补且互斥的事件。在一个互斥的集合中,一次只能发生一个事件,比如说掷骰子不可能同时掷出两个数字。
例子
- 上面所提到由“投出1、投出2、投出3、投出4、投出5、投出6”所构成的集合既是互斥的,又是互补的。
- 仅由“投出1和投出6”构成的事件是互斥的,他们不可能同时发生;但不是互补的,因为还能投出2、3、4、5。
- 事件“投出偶数(2、4或6)”和“投出的不是6(1、2、3、4或5)”在总体上是互补的,因为他们的并集包括了所有可能的情况。但并不互斥,因为当投出2或4时,两个事件同时发生了。
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