Probability - Addition Rule for Overlapping Events

Box \(A\) contains \(6\) balls numbered \(1, 2, 2, 2, 5, 7\).

Box \(B\) contains \(4\) balls numbered \(1, 4, 4, 7\).

Box \(C\) contains \(3\) balls numbered \(3, 4, 6\).

One ball is removed at random from each box.

1. Show that the probability that each of the three numbers obtained is greater than \(3\) is \(\frac{1}{6}\).[1]
2. Find the probability that each of the three numbers obtained is greater than \(3\) or the sum of the three numbers obtained is \(13\) (or both).[4]