(i) To find the probability that a taxi arrives late, we use the law of total probability. Let L be the event that a taxi arrives late. We have:

\(P(L) = P(A) \cdot P(L|A) + P(B) \cdot P(L|B) + P(C) \cdot P(L|C)\)

Substituting the given probabilities:

\(P(L) = 0.5 \times 0.04 + 0.3 \times 0.06 + 0.2 \times 0.17\)

\(P(L) = 0.02 + 0.018 + 0.034 = 0.072\)

Thus, the probability that a taxi arrives late is 0.072.

(ii) To find the conditional probability that Andrea rang company B given that the taxi arrives late, we use Bayes' theorem:

\(P(B|L) = \frac{P(B) \cdot P(L|B)}{P(L)}\)

Substituting the known values:

\(P(B|L) = \frac{0.3 \times 0.06}{0.072}\)

\(P(B|L) = \frac{0.018}{0.072} = 0.25\)

Thus, the conditional probability that she rang company B is 0.25.