Consider a fair tetrahedral die whose sides are painted red, green, blue, and white. Roll the die. Let ${X}_{r},{X}_{g},{X}_{b}$ be the events that die falls on a side that have red, green, and blue color components, respectively. Then

$P({X}_{r})=P({X}_{g})$ 
$=P({X}_{b})={\displaystyle \frac{1}{2}},$ 


$P({X}_{r}\cap {X}_{g})=P({X}_{w})$ 
$={\displaystyle \frac{1}{4}}=P({X}_{r})P({X}_{g}),$ 

but 

$P({X}_{r}\cap {X}_{g}\cap {X}_{b})={\displaystyle \frac{1}{4}}$ 
$\ne {\displaystyle \frac{1}{8}}=P({X}_{r})P({X}_{g})P({X}_{b}).$ 
