Total-score, at-least-one and conditional probabilities for a four-sided and a six-sided die

A fair four-sided die with faces numbered \(1\) to \(4\) and a fair six-sided die with faces numbered \(1\) to \(6\) are rolled together. The total of the two scores is \(T\).

1. Find the probability that \(T\) is greater than \(6\).[2]
2. Find the probability that at least one of the dice shows a \(4\).[2]
3. Given that \(T\) is greater than \(6\), find the probability that at least one of the dice shows a \(4\).[3]