Решение задачи N3680 теория вероятностей Байеса

3680. Three machines make parts that go to a common conveyor. The performance of the first, second and third machines are referred to as 13:14:10. The probability that the part made by the first machine is of excellent quality is 0.9; for the second and third automata, these probabilities are equal to 0.8 and 0.7, respectively. Find the probability that: a) at random, the part taken from the conveyor is not of excellent quality; b) the part was made by the second machine, if at random the part taken from the conveyor is not of excellent quality.

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