(a) The total probability that Kino is late is given by:

\(0.2x + 0.1 \times 2x + 0.7 \times 0.25 = 0.235\)

Simplifying, we have:

\(0.2x + 0.2x + 0.175 = 0.235\)

\(0.4x + 0.175 = 0.235\)

Subtract 0.175 from both sides:

\(0.4x = 0.06\)

Divide by 0.4:

\(x = 0.15\)

(b) We need to find \(P(\text{car} | \text{not late})\).

\(P(\text{car} | \text{not late}) = \frac{P(\text{car and not late})}{P(\text{not late})}\)

\(P(\text{car and not late}) = 0.1 \times (1 - 2x) = 0.1 \times (1 - 0.3) = 0.1 \times 0.7 = 0.07\)

\(P(\text{not late}) = 1 - 0.235 = 0.765\)

Thus,

\(P(\text{car} | \text{not late}) = \frac{0.07}{0.765} = 0.0915\)

Expressed as a fraction, \(\frac{0.07}{0.765} = \frac{70}{765} = \frac{14}{153}\).