Solving problem N4067 Bayesian probability theory

Solving problem N4067 Bayesian probability theory

4067. The number of trucks traveling along the highway on which the gas station stands refers to the number of cars passing along the same highway as 5: 2. The probability that a passing truck will refuel is 0.02. For a passenger car, this probability is 0.05. Find probabilities of events:
1. A randomly selected driving car will refuel (Event A).
2. A car that has arrived at a gas station is a truck (event H1).

Additional information:

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