Suppose that a factory has two machines, Machine A and Machine B, both producing Phone touch screens. 40% of their touch screens come from Machine A and 60% of their touch screens come from Machine B....

Suppose that a factory has two machines, Machine A and Machine B, both producing Phone touch screens. 40% of their touch screens come from Machine A and 60% of their touch screens come from Machine B. 10% of the touch screens produced by Machine A are defective and 5% of the touch screens from Machine B are defective. If randomly touch screen has been chosen and it is defective, what is the probability that it came from machine A? (Show your work)