Solving problem N3946 Bayesian probability theory

Solving problem N3946 Bayesian probability theory

3946. An average of 40% of hours with defect A, 25% with defect B and 35% with defect C arrive at the watch workshop. The probability of repairing hours with defect A is 0.6, with defect B 0.7, with defect C 0.8 Find the probability that: a) the watch received for repair will be completely repaired; b) the fully repaired watch had a defect A.

Additional information:

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