To determine if events S and T are independent, we need to check if \(P(S \cap T) = P(S) \times P(T)\).

First, calculate \(P(S)\):

The possible outcomes for the sum to be 4 are (1,3), (2,2), and (3,1). Thus, \(P(S) = \frac{3}{16}\).

Next, calculate \(P(T)\):

The product is odd if both numbers are odd. The possible outcomes are (1,1), (1,3), (3,1), and (3,3). Thus, \(P(T) = \frac{4}{16}\).

Now, calculate \(P(S \cap T)\):

The outcomes that satisfy both events are (1,3) and (3,1). Thus, \(P(S \cap T) = \frac{2}{16}\).

Check independence:

\(P(S) \times P(T) = \frac{3}{16} \times \frac{4}{16} = \frac{12}{256} = \frac{3}{64}\).

Since \(\frac{3}{64} \neq \frac{2}{16}\), events S and T are not independent.

For exclusivity, events are exclusive if \(P(S \cap T) = 0\).

Since \(P(S \cap T) = \frac{2}{16} \neq 0\), events S and T are not exclusive.