Solving problem N4018 Bayesian probability theory

Solving problem N4018 Bayesian probability theory

4018. The number of trucks passing along the highway on which the gas station stands is one of the cars passing along the same highway as 13:11. The probability that a truck will refuel is 0.1; for a passenger car, this probability is 0.2. A car drove up to the gas station for refueling. Find the probability that this is a truck.

Additional information:

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