explanation for multiplication rule for independent events with|A| > 2 This is my assumption:
if A is the set of events:
$ A = \{A1, A2, A3\} $
And i want to find out if they are mutually independent, all i have to do is check that the two following conditions hold true:
$ r1: P(A1 \cap A2) = P(A1)P(A2) $
$ \land $
$ r2: P(A1 \cap A2 \cap A3) = P(A1)P(A2)P(A3)$
Am i right?
thank you very much

A finite set of events is mutually independent if and only if every event is independent of any intersection of the other events — that is, if and only if for every $n$-element subset ${A_i}$,
$$
\mathrm{P}\left(\bigcap_{i=1}^n A_i\right)=\prod_{i=1}^n \mathrm{P}(A_i)
$$
(see here). Hence, we also have to check that $P(A_1\cap A_3)=P(A_1)P(A_3)$ and $P(A_2\cap A_3)=P(A_2)P(A_3)$.
