example of pairwise independent events that are not totally independent

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).$