Solving problem N4036 Bayesian probability theory

Solving problem N4036 Bayesian probability theory

4036. The number of trucks driving along the highway on which the gas station stands is one of the cars passing along the same highway as 2: 1. It is known that, on average, one of 30 trucks and one of 25 passenger cars drive up to a gas station for refueling. Find the probabilities of the following events: a) a truck will drive along the highway and it will refuel; b) a car will drive along the highway and it will refuel; c) a car driving along a highway will refuel.

Additional information:

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