3 A fair eight-sided die has faces marked \(1,2,3,4,5,6,7,8\). The score when the die is thrown is the number on the face the die lands on. The die is thrown twice.
- Event \(R\) is 'one of the scores is exactly 3 greater than the other score'.
- Event \(S\) is 'the product of the scores is more than 19'.
- Find the probability of \(R\).
- Find the probability of \(S\).
- Determine whether events \(R\) and \(S\) are independent. Justify your answer.