6 There are three sets of traffic lights on Karinne's journey to work. The independent probabilities that Karinne has to stop at the first, second and third set of lights are \(0.4,0.8\) and 0.3 respectively.
- Draw a tree diagram to show this information.
- Find the probability that Karinne has to stop at each of the first two sets of lights but does not have to stop at the third set.
- Find the probability that Karinne has to stop at exactly two of the three sets of lights.
- Find the probability that Karinne has to stop at the first set of lights, given that she has to stop at exactly two sets of lights.