Решение задачи N4041 теория вероятностей Байеса

4041. The shop receives similar products from three plants, with the i-th (i = 1,2,3) plant supplying mi percent of the products (m1 = 50%, m2 = 20%, m3 = 30%). Among the products of the i-th plant, ni percent are first-rate (90%, 80%, 90%). Bought one product. It turned out to be first-rate. Determine the probability that the purchased product is released by the 3rd plant.

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