Solving problem N4065 Bayesian probability theory

Solving problem N4065 Bayesian probability theory

4065. Cars and trucks are passing by the gas station. Among them, trucks are 45%. The probability that a passing car arrives at a gas station for trucks is 0.2, and for cars it is 0.3. A car drove up to a gas station to a gas station. Find the probability that it is passenger.

Additional information:

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