6 A fair tetrahedral die has four triangular faces, numbered \(1,2,3\) and 4 . The score when this die is thrown is the number on the face that the die lands on. This die is thrown three times. The random variable \(X\) is the sum of the three scores.

1. Show that \(\mathrm { P } ( X = 9 ) = \frac { 10 } { 64 }\).
2. Copy and complete the probability distribution table for \(X\).

   \(x\)	3	4	5	6	7	8	9	10	11	12
   \(\mathrm { P } ( X = x )\)	\(\frac { 1 } { 64 }\)	\(\frac { 3 } { 64 }\)			\(\frac { 12 } { 64 }\)

3. Event \(R\) is 'the sum of the three scores is 9 '. Event \(S\) is 'the product of the three scores is 16 '. Determine whether events \(R\) and \(S\) are independent, showing your working.