A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event,

When a die is thrown, the sample space (S) is

S = {1, 2, 3, 4, 5, 6}

Let A: the number is even = {2, 4, 6}

$\Rightarrow \mathrm{P}(\mathrm{A})=\frac{3}{6}=\frac{1}{2}$

B: the number is red $=\{1,2,3\}$

$\Rightarrow \mathrm{P}(\mathrm{B})=\frac{3}{6}=\frac{1}{2}$

$\therefore \mathrm{A} \cap \mathrm{B}=\{2\}$

$P(A B)=P(A \cap B)=\frac{1}{6}$

$P(A) \cdot P(B)=\frac{1}{2} \times \frac{1}{2}=\frac{1}{4} \neq \frac{1}{6}$

$\Rightarrow \mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{B}) \neq \mathrm{P}(\mathrm{AB})$

Therefore, A and B are not independent.