"Pairwise independent" is weaker that "independent" Can someone please give me a reference  to an (simple, realworld, i.e. not constructed) example of a discrete probability space such that there are three events in it that are pairwise independent but all three together are not independent (although I wouldn't mind, if someone would give me the example as an answer).

The standard example involves tossing $2$ fair coins. For a more symmetrical example, toss $3$ fair coins. Let $A$ be the event Toss $1$ and Toss $2$ give the same result, $B$ be the event Toss $2$ and Toss $3$ give the same result, and $C$ the event Toss $3$ and Toss $1$ give the same result. 
We have $\Pr(A)=\Pr(B)=\Pr(C)=\frac{1}{2}$ and $\Pr(A\cap B)=\Pr(B\cap C)=\Pr(C\cap A)=\frac{1}{4}$. 
However, it is clear that $A$, $B$, and $C$ are not mutually independent. 
