Solving problem N4048 Bayesian probability theory

4048. The shop receives the same type of products from three factories, with the 1st plant supplying 10% of the products, the 2nd plant - 50%, the 3rd plant - 40%. Among products of the 1st plant, 70% are top-notch, among products of the 2nd - 90%, of the 3rd - 80%. Bought one product. It turned out to be first-rate. Determine the probability that the purchased product is produced by the 1st plant.