Airline services provide various packages for their customers booking during holiday season. There are 20%, 45% and 35% of the customers booked for Package A, Package B and Package C respectively. Given, the probability of Package A, Package B and Package C experienced with bad services are 0.002, 0.001 and 0.003.

Based on the above situation, answer the following questions:

a) Construct a tree diagram based on the situation given and determine their associated probabilities, including the intersection probabilities together with the outcomes.

b) Based on the answer in (i), determine the probability that a customer experienced with a good service from the airlines.

c) Given that the package is operating smoothly, what is the probability that it is in Package B?