Solving problem N3932 Bayesian probability theory

3932. There are three factories producing the same products. At the same time, the 1st plant produces 25%, the 2nd plant - 35%, and the 3rd plant - 40% of all products produced. Marriage is 5% of the products of the 1st plant, 3% of the products of the 2nd and 4% of the products of the 3rd plant. All products are mixed and marketed. Find: a) the probability of buying a defective product; b) the conditional probability that the purchased product is manufactured by the 1st plant, if this product is defective.