Solving problem N3938 Bayesian probability theory

3938. Watches are made in three factories and go to the store. The first plant produces 40% of incoming products, the second - 45%, the third - 15%. In the production of the first plant, 80% of hours rush, in the second - 70%, in the third - 90%. Watches bought in this store are in a hurry. What is the probability that they are produced at the first plant?