3914. On three machines under the same and independent conditions, parts of the same name are manufactured. On the first machine is made 10%, on the second - 30%, and on the third 60% of all parts. For each part, the probability of being faultless is 0.7 if it is made on the first machine; 0.8, if it is made on the second machine; 0.9 if it is made on the third machine. Find the probability that a part taken at random will be defect free.

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