A company that produces a particular machine component has 3 factories, one each in ...

A company that produces a particular machine component has 3 factories, one each in Buffalo, Detroit, and Pittsburgh. 58% of the components produced come from the Buffalo factory, 23% of the components come from the Detroit factory, and 19% of the components come from the Pittsburgh factory. It is known that 1.0% of the components from the Buffalo factory, 0.9% of the components from the Detroit factory, and 1.2% of the components from the Pittsburgh factory are defective. Given that a component is selected at random and is found to be defective, what is the probability that the component was made in Buffalo?