3 An investigation was carried out into the type of vehicle being driven when its driver was caught speeding. The investigation was restricted to drivers who were caught speeding when driving vehicles with at least 4 wheels. An analysis of the results showed that \(65 \%\) were driving cars ( C ), \(20 \%\) were driving vans (V) and 15\% were driving lorries (L). Of those driving cars, \(30 \%\) were caught by fixed speed cameras (F), 55\% were caught by mobile speed cameras (M) and 15\% were caught by average speed cameras (A). Of those driving vans, \(35 \%\) were caught by fixed speed cameras (F), \(45 \%\) were caught by mobile speed cameras (M) and 20\% were caught by average speed cameras (A). Of those driving lorries, \(10 \%\) were caught by fixed speed cameras \(( \mathrm { F } )\), \(65 \%\) were caught by mobile speed cameras (M) and \(25 \%\) were caught by average speed cameras (A).

1. Represent this information by a tree diagram on which are shown labels and percentages or probabilities.
2. Hence, or otherwise, calculate the probability that a driver, selected at random from those caught speeding:
   1. was driving either a car or a lorry and was caught by a mobile speed camera;
   2. was driving a lorry, given that the driver was caught by an average speed camera;
   3. was not caught by a fixed speed camera, given that the driver was not driving a car.
      [0pt] [8 marks]
3. Three drivers were selected at random from those caught speeding by fixed speed cameras. Calculate the probability that they were driving three different types of vehicle.
   [0pt] [4 marks]