(a) Let the probability that Alexa arrives late be \(P(\text{late})\). We know that \(P(\text{not late}) = 0.48\).

Using the total probability theorem, \(P(\text{not late}) = 0.4 \times 0.45 + 0.35 \times 0.3 + 0.25 \times (1-x) = 0.48\).

Calculating, \(0.18 + 0.105 + 0.25(1-x) = 0.48\).

\(0.285 + 0.25 - 0.25x = 0.48\).

\(0.535 - 0.25x = 0.48\).

\(0.25x = 0.535 - 0.48\).

\(0.25x = 0.055\).

\(x = \frac{0.055}{0.25} = 0.22\).

(b) To find \(P(\text{train} | \text{late})\), use Bayes' theorem:

\(P(\text{train} | \text{late}) = \frac{P(\text{train} \cap \text{late})}{P(\text{late})}\).

\(P(\text{train} \cap \text{late}) = 0.35 \times 0.7 = 0.245\).

\(P(\text{late}) = 1 - P(\text{not late}) = 0.52\).

Thus, \(P(\text{train} | \text{late}) = \frac{0.245}{0.52} = \frac{49}{104}\) or 0.471.