Solving problem N4039 Bayesian probability theory

Solving problem N4039 Bayesian probability theory

4039. Passenger cars at the gas station passes four times more than trucks. The probability that a passing car arrives at a gas station is 0.05 for a truck, and 0.15 for a car. a) A car is approaching the place where the gas station is located. Determine the likelihood that she will drive to the gas station. b) A refueled car just left the gas station. What is the likelihood that it was a truck?

Additional information:

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