Solving problem N4064 Bayesian probability theory

Solving problem N4064 Bayesian probability theory

4064. Past the gas station passing cars and trucks. Among them, 40% of cars. The probability that a passing car arrives at a gas station for cars is 0.2, and for trucks it is 0.1. A car drove up to a gas station to a gas station. Find the probability that she is freight.

Additional information:

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