A foreman for an injection-molding firm admits that on 31% of his shifts, he forgets to shut off the injection machine on his line.

A foreman for an injection-molding firm admits that on 31% 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?