A die marked $$1,\,2,\,3$$   in red and $$4,\,5,\,6$$   in green is tossed. Let $$A$$ be the event, "the number is even", and $$B$$ be the event, "the number is red" then;

Solution :
When a die is thrown, the sample space $$\left( S \right)$$ is
$$S = \left\{ {1,\,2,\,3,\,4,\,5,\,6} \right\}$$
Let $$A :$$  the number is even $$ = \left\{ {2,\,4,\,6} \right\}$$
$$\therefore \,P\left( A \right) = \frac{3}{6} = \frac{1}{2}$$
$$B :$$  the number is red $$ = \left\{ {1,\,2,\,3} \right\}$$
$$\eqalign{ & \therefore \,P\left( B \right) = \frac{3}{6} = \frac{1}{2} \cr & A \cap B = \left\{ 2 \right\},\,P\left( {A \cap B} \right) = \frac{1}{6} \cr & {\text{or }}P\left( A \right).P\left( B \right) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \ne \frac{1}{6} \cr} $$