Решение задачи N3818 теория вероятностей Байеса

3818. In the workshop on the three machines manufactured the same type of parts. The probability of manufacturing a part on the first machine is 0.5, on the second - 0.3, on the third - 0.2. The probability of manufacturing a defective part on the first machine is 0.2; at the second 0.3; in the third 0.1. Find the probability that the selected part will be standard at random. What is the probability that this standard part is made on the third machine?

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