Solving problem N4017 Bayesian probability theory

Solving problem N4017 Bayesian probability theory

4017. 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 2: 3. It is known that, on average, one out of thirty trucks and two out of fifty cars drive up to a gas station to refuel. What is the probability that:
a) a truck drove up to the gas station and it will refuel;
b) a passenger car drove up to the gas station and it will refuel;
c) the car which approached the gas station will be refueled.

Additional information:

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