Решение задачи N3915 теория вероятностей Байеса

3915. On three machines with identical and independent conditions, parts of the same name are manufactured. On the first machine make 10%, on the second - 30%, on the third - 60% of all parts. The probability of each part to be faultless is 0.7, if it is made on the first machine, 0.8 - if on the second machine, and 0.9 - if on the third machine. The detail taken at random turned out to be faultless. Find the probability that it is made on 2 machines.

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