Solving problem N3944 Bayesian probability theory

Solving problem N3944 Bayesian probability theory

3944. The watches entering the store are produced by three factories: 70% comes from the first, 20% from the second, and 10% from the third. The reject rate at each of the plants is 3%, 2% and 4% respectively. Find: 1) the probability that the purchased watches are defective; 2) the probability that these defective watches are made at the 2nd plant.

Additional information:

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