2022 ACJC J2 MYE P1 Q11

A fair six-sided die and another fair tetrahedral (4 sided) die are thrown together once. \(S\) is the absolute difference of the scores of the two dice.

1. Find the probability distribution of \(S\).[3]

If \({{S}_{1}}\), \({{S}_{2}}\), \({{S}_{3}}\) are independent observations of \(S\), find

2. \(\mathrm{P}\left( {{S}_{1}}=\left. 2 \right|{{S}_{1}}+{{S}_{2}}+{{S}_{3}}=3 \right)\).[3]