Solving problem N3945 Bayesian probability theory

Solving problem N3945 Bayesian probability theory

3945. The clock shop comes from three factories, with 40% coming from the first factory, 35% from the second, and 25% from the third. The probability of marriage in the first factory is 0.06, in the second - 0.07, and in the third - 0.08. The selected watches were defective. What is the probability that this watch is a) from the first factory? b) from the second factory? c) from the third factory?

Additional information:

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