Solution of problem N3914 probability theory

Solution of problem N3914 probability theory

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.

Additional information:

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