Frequently the nature of an experiment suggests that two events and should be assumed independent. This is the case, for example, if a manufacturer receives a circuit board from each of two different suppliers, each board is tested on arrival, and first is defective and second is defective . If , it should also be the case that ; knowing the condition of the second board shouldn’t provide information about the condition of the first. The probability that both events will occur is easily calculated from the individual event probabilities when the events are independent.
通常实验的性质暗示两个事件 和 应该被假定为独立的。例如，如果一个制造商从两个不同的供应商那里各接收一块电路板，每块板在到达时都进行测试，且 第一块是次品 和 第二块是次品 。如果 ，那么 也应该是这样的情况；了解第二块板的情况不应当提供关于第一块板情况的信息。当事件独立时，两个事件同时发生的概率可以很容易地从各自事件的概率计算得出。
independence
and are independent if and only if (iff)
命题 和 是独立的当且仅当（iff）
The verification of this multiplication rule is as follows:
本乘法规则的验证如下：
where the second equality in Equation (2.9) is valid iff and are independent. Equivalence of independence and Equation (2.8) imply that the latter can be used as a definition of independence.其中方程（2.9）中的第二个等式在 和 独立时有效。独立性与方程（2.8）的等价性意味着后者可以作为独立性的定义使用。