Solving problem N3720 Bayesian probability theory

Solving problem N3720 Bayesian probability theory

3720. Among the cases coming to the regional court from the Kirov district are 15% criminal, from the Soviet - 10%, from Trusovsky - 8%. The numbers of cases brought to the court from the Soviet, Kirov, Trusovsky district courts are 2: 5: 3. Find the probability that a case is taken at random:
1) not criminal;
2) and came from the Trusovsky District Court.

Additional information:

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