Solving problem N4047 Bayesian probability theory

4047. The shop receives similar products from three plants, with the i-th (i = 1,2,3) plant supplying mi percent of the products (m1 = 20%, m2 = 40%, m3 = 40%). Among the products of the i-th plant, ni percent are first-rate (90%, 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.