Solving problem N3721 Bayesian probability theory

Solving problem N3721 Bayesian probability theory

3721. On average, the regional court receives 50% of cases from the Leninsky court, 28% from Trusovsky, and the rest from the Kirovsky court. The probability that the Lenin court case will not be returned is 0.75; for Trusovsky and Kirov, these probabilities are 0.84 and 0.92, respectively. What is the probability that:
1) the case taken at random will be returned;
2) and it came from the Kirov court.

Additional information:

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