Solving problem N4062 Bayesian probability theory

Solving problem N4062 Bayesian probability theory

4062. Past the gas station passing cars and trucks. Among them, 60% of trucks. The probability that a passing car will arrive at a gas station is 0.1 for trucks, and 0.2 for cars. A passing car drove up to a gas station for a gas station. Find the probability that this is a passenger car.

Additional information:

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