A box of similar products is produced by three factories, 50% of which are produced by the first factory and 25% by each of the remaining two. It is also known that 2%, 4% and 5% of the products produced by the first, second and third factories are defective respectively, and any one product is taken from the box. Please finish the following problems. (1) The probability that the product taken is defective. (2) If the product taken is known to be defective, the probability that it was produced in the first factory.
