1. **Stating the problem:** Mark travels by train or bus. - Probability train is late: $0.15$ - Probability bus is on time: $0.8$ - Probability Mark chooses bus: $0.3$ We need to: (i) Complete a tree diagram. (ii) Find the probability Mark arrives on time. 2. **Tree diagram setup:** - Mark chooses bus with probability $0.3$, so train with probability $1 - 0.3 = 0.7$. - For train: probability late $= 0.15$, so on time $= 1 - 0.15 = 0.85$. - For bus: probability on time $= 0.8$, so late $= 1 - 0.8 = 0.2$. 3. **Tree diagram probabilities:** - Train on time: $0.7 \times 0.85 = 0.595$ - Train late: $0.7 \times 0.15 = 0.105$ - Bus on time: $0.3 \times 0.8 = 0.24$ - Bus late: $0.3 \times 0.2 = 0.06$ 4. **Finding probability Mark arrives on time:** $$P(\text{on time}) = P(\text{train on time}) + P(\text{bus on time}) = 0.595 + 0.24 = 0.835$$ **Final answer:** The probability Mark arrives on time is $0.835$.