Independent 獨立

Definition
P(EF) = P(E)P(F) 成立, 則稱兩事件 EF 獨立(independent). 不獨立的兩事件 EF 則稱之為相依(dependent).

Example

Example

Proposition
EF 為獨立事件 , 則 EFc 也是獨立事件.
Proof:

or equivalently,

Thus, if E is independent of F, then the probability of E's occurrence is unchanged by information as to whether or not F has occurred.