Die frequencies and additional throws

Core stretch

After 25 throws of a die, scores 1–6 have frequencies 6, 4, 6, 4, 3, 2.

1. State the mode(s).[1]
2. Find the lowest possible 26th score that leaves the median equal to 3.[1]
3. Suppose that lowest score occurs, then the die is thrown twice more. If the mean after 28 throws is 3, list the possible unordered pairs of final two scores.[2]