Aforeman for an injection-molding firm admits that on 45% of his shifts, he forgets to shut off the injection machine on his line. this causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 3% to 15%. the plant manager randomly selects a molding from the early morning run and discovers it is defective. what is the probability that the foreman forgot to shut off the machine the previous night?