Dan either walks or cycles to school. The probability that he cycles is \(\frac13\).

(a) Write down the probability that he walks. [1]

When he cycles, the probability he is late is \(\frac18\). When he walks, the probability he is late is \(\frac38\).

(b) Complete the tree diagram. [2]

(c(i)) Calculate the probability that Dan cycles and is late. [2]

(c(ii)) Calculate the probability that Dan is not late. [3]