Let $A$ and $B$ be two events and $p$ and $q$ be their corresponding probabilities. One of the properties of surprise function is:
$$S(AB) = S(A) + S(B)$$
Which seems to be fine if the two events are independent.
However, let's take following example: $A$ indicates getting an odd number when rolling a dice and $B$ indicates getting $3$ when rolling a die. These two events are clearly dependent. How does the above property works? because clearly $P(AB)$ is not equal to $(1/6)*(1/2)$. What am I missing here?