Solving problem N4044 Bayesian probability theory

4044. The shop receives the same type of products from three plants, with the i-th (i = 1,2,3) plant supplying mi percent of the products (m1 = 30%, m2 = 30%, m3 = 40%). Among the products of the i-th plant, ni percent are first-rate (70%, 70%, 80%). Bought one product. It turned out to be first-rate. Determine the probability that the purchased product is released by the 3rd plant.