(i) The tree diagram is drawn with the following branches:

• First set of branches for the type of message: text (0.3), email (0.2), social media (0.5).
• Second set of branches for replies:
• Text: reply (0.4), no reply (0.6).
• Email: reply (0.15), no reply (0.85).
• Social media: reply (0.6), no reply (0.4).

(ii) To find the probability that the message was an email given no immediate reply, use Bayes' theorem:

\(P(\text{email} \mid \text{NR}) = \frac{P(\text{email} \cap \text{NR})}{P(\text{NR})}\)

Calculate \(P(\text{email} \cap \text{NR}) = 0.2 \times 0.85 = 0.17\).

Calculate \(P(\text{NR}) = 0.3 \times 0.6 + 0.2 \times 0.85 + 0.5 \times 0.4 = 0.18 + 0.17 + 0.2 = 0.55\).

Thus, \(P(\text{email} \mid \text{NR}) = \frac{0.17}{0.55} = \frac{17}{55} \approx 0.309\)