Solving problem N4015 Bayesian probability theory

Solving problem N4015 Bayesian probability theory

4015. The number of trucks traveling along the highway on which the gas station stands is one of the cars passing along the same highway as 3: 5. It is known that, on average, one out of 30 trucks and two out of 50 passenger cars drive up to a gas station to refuel. What is the probability that: a) the car that approached the gas station will refuel; b) there is a passenger car at the gas station; c) is there a truck at the gas station?

Additional information:

Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)