**What three mathematical statements are equivalent to the statement that $A$ and $B$ are independent?** The three mathematical statements which are equivalent to the statement that $A$ and $B$ are independent are: 1. $P(A|B)=P(A)$. 2. $P(A\cap B)=P(A)P(B)$. 3. $P(B|A)=P(B)$. **Is independence a symmetric relationship?** *Yes*, independence is a symmetric relationship. ... **What is mathematical statement is equivalent to the statement that $A$, $B$, and $C$ are mutually independent?** The mathematical statement which is equivalent to the statement that $A$, $B$, and $C$ are mutually independent is: $P(A\cap B\cap C)=P(A)P(B)P(C)$ ... **Are two events with nonzero probability mutually exclusive (disjoint) if they're independent?** *No*, two events with nonzero probability aren't mutually exclusive if they're independent. **Are mutually exclusive (disjoint) events independent?** *No*, mutually exclusive (disjoint) events aren't independent. ...