Solving problem N4014 Bayesian probability theory

Solving problem N4014 Bayesian probability theory

4014. Trucks, buses and cars pass by the highway near which the gas station stands; their ratio is 2: 3: 5. The probability that a truck will be refueled is 0.3; for buses and cars, refueling probabilities are 0.2 and 0.1, respectively. What is the probability that a car passing along a highway will stop at a gas station? At the gas station drove the car. What is the probability that this is a truck?

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