2 On a rail route between two stations, A and \(\mathrm { B } , 90 \%\) of trains leave A on time and \(10 \%\) of trains leave A late. Of those trains that leave A on time, \(15 \%\) arrive at B early, \(75 \%\) arrive on time and \(10 \%\) arrive late. Of those trains that leave A late, \(35 \%\) arrive at B on time and \(65 \%\) arrive late.

1. Represent this information by a fully-labelled tree diagram.
2. Hence, or otherwise, calculate the probability that a train:
   1. arrives at B early or on time;
   2. left A on time, given that it arrived at B on time;
   3. left A late, given that it was not late in arriving at B .
3. Two trains arrive late at B. Assuming that their journey times are independent, calculate the probability that exactly one train left A on time.