In a certain factory, machines I, II, III are all producing springs of the same length. Machines I, II, and III produce 1%, 4% and 2% defective springs, respectively. Of the total production of springs in the factory, Machine I produces 30%, Machine II products 25%, and Machine III produces 45%. If one spring is selected at random from the total springs produced in a given day, determine the probability that it is defective.
I know that this must involve the intersection of the percentages of defective springs given those produced by the machines, but I can't put it together. Will someone please help me get started? Thanks.