3 Ellie throws two fair tetrahedral dice, each with faces numbered 1, 2, 3 and 4. She notes the numbers on the faces that the dice land on. Event \(S\) is 'the sum of the two numbers is 4 '. Event \(T\) is 'the product of the two numbers is an odd number'.
- Determine whether events \(S\) and \(T\) are independent, showing your working.
- Are events \(S\) and \(T\) exclusive? Justify your answer.