Solving problem N4001 Bayesian probability theory

4001. The store receives the same type of products from three factories, with the 1st plant supplying 50% of the products, the 2nd plant - 30%, the 3rd plant - 20%. Among the products of the 1st plant, 70% are top-notch, among the products of the 2nd - 80%, of the 3rd - 90%. Bought one product. It turned out to be first-rate. Determine the probability that the purchased product is produced by the 1st plant.