(i) The tree diagram should have branches for each call attempt with probabilities 0.5 for Answered (A) and 0.5 for Unanswered (U). There should be 4 levels of branches, representing up to 4 attempts.

(ii) The probability distribution table is completed as follows:

(iii) The expected number of unanswered calls \(E(X)\) is calculated as:

\(E(X) = \sum x \cdot P(X = x) = 0 \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} + 2 \cdot \frac{1}{8} + 3 \cdot \frac{1}{16} + 4 \cdot \frac{1}{16}\)

\(E(X) = 0 + \frac{1}{4} + \frac{2}{8} + \frac{3}{16} + \frac{4}{16}\)

\(E(X) = \frac{1}{4} + \frac{1}{4} + \frac{3}{16} + \frac{4}{16}\)

\(E(X) = \frac{1}{2} + \frac{7}{16} = \frac{15}{16}\)

Thus, \(E(X) = \frac{15}{16}\) or approximately 0.938 or 0.9375.