Решение задачи N3888 теория вероятностей Байеса

3888. The collector receives 50% of the details of Plant No. 1, 30% of Plant No. 2, 20% of Plant No. 3. The probability that a part of factory No. 1 is of excellent quality is 0.7; plant number 2 - 0.8; Plant number 3 - 0.9. The detail taken at random turned out to be of excellent quality. Find the probability that this part is made by factory number 1.

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