Решение задачи N3913 теория вероятностей Байеса

3913. In a bolts factory, the first machine produces 25%, the second - 35%, and the third - 40% of all bolts. In their products, the defect is respectively 5, 4 and 7%. a) Find the probability that a randomly selected bolt was defective. b) A randomly selected bolt was found to be defective. Find the probability that it is manufactured by the first machine.

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