Solving problem N4066 Bayesian probability theory

Solving problem N4066 Bayesian probability theory

4066. Passenger cars near the gas station drives 2 times more than trucks. The probability that a passenger car will drive up to a gas station is 0.2 and a cargo car is 0.1.
a) a car pulls up to the gas station, what is the probability that it will stop at the gas station.
b) the car just left the gas station, what is the probability that the car is passenger.

Additional information:

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