(i) The tree diagram is constructed as follows:

• First branch: Tea (T) with probability 0.65, Coffee (C) with probability 0.28, Hot Chocolate (HC) with probability 0.07.
• Second branch for Tea: Milk (M) with probability 0.8, No Milk (NM) with probability 0.2.
• Second branch for Coffee: Milk (M) with probability 0.5, No Milk (NM) with probability 0.5.
• Second branch for Hot Chocolate: Milk (M) with probability 1, No Milk (NM) with probability 0.

(ii) To find the probability that Ayman’s breakfast drink is coffee, given that his drink has milk in it, we use Bayes' theorem:

\(P(C \mid \text{milk}) = \frac{P(C \cap \text{milk})}{P(\text{milk})}\)

Calculate \(P(C \cap \text{milk})\):

\(P(C \cap \text{milk}) = 0.28 \times 0.5 = 0.14\)

Calculate \(P(\text{milk})\):

\(P(\text{milk}) = (0.65 \times 0.8) + (0.28 \times 0.5) + (0.07 \times 1) = 0.52 + 0.14 + 0.07 = 0.73\)

Substitute these into the formula:

\(P(C \mid \text{milk}) = \frac{0.14}{0.73} \approx 0.192\)