Total Probability from Travel Choices

Angel either walks or cycles to school every morning. The probability that she walks is \(\frac{2}{3}\). When she walks, the probability that she is late for school is \(\frac{4}{9}\). When she cycles, the probability that she is late for school is \(\frac{1}{9}\). Find the probability that on a particular morning,

1. Angel walks and is not late for school,
2. she is late for school.