Solving problem N4026 Bayesian probability theory

4026. The same type of products come from three factories to the store, with the 1st plant supplying 60% of the products, the 2nd plant - 10%, the 3rd plant - 30%. Among the products of the 1st plant 80% are first-class, among the 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.