Solving problem N4031 Bayesian probability theory

Solving problem N4031 Bayesian probability theory

4031. The number of trucks traveling along the highway on which the gas station stands is one of 3: 7 cars. The probability that a truck will refuel at this gas station is 0.1 and a passenger car is 0.2. Find the probability that a truck will drive up to a gas station for refueling.

Additional information:

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