2. On a randomly chosen day the probability that Bill travels to school by car, by bicycle or on foot is \(\frac { 1 } { 2 } , \frac { 1 } { 6 }\) and \(\frac { 1 } { 3 }\) respectively. The probability of being late when using these methods of travel is \(\frac { 1 } { 5 } , \frac { 2 } { 5 }\) and \(\frac { 1 } { 10 }\) respectively.

1. Draw a tree diagram to represent this information.
2. Find the probability that on a randomly chosen day
   1. Bill travels by foot and is late,
   2. Bill is not late.
3. Given that Bill is late, find the probability that he did not travel on foot.