Tree diagram for two rolls of an eight-sided die and a binomial count of how often exactly one multiple of four occurs

A fair eight-sided die has faces numbered \(1\) to \(8\). The die is rolled twice. Let \(M\) be the event that the score on a roll is a multiple of \(4\).

1. Copy and complete the tree diagram below, which shows the possible outcomes of the two rolls.[3]

Let \(E\) be the event that exactly one of the two rolls gives a multiple of \(4\).

2. Find \(\mathrm{P}(E)\).[3]

The die is rolled twice on each of \(6\) separate turns.

3. Find the probability that \(E\) occurs on exactly \(3\) of the \(6\) turns.[3]
4. Find the probability that \(E\) occurs on at least \(3\) of the \(6\) turns.[3]