Question
A factory has a total of three manufacturing units, M_1, M_2, and M_3, which produce bulbs independent of each other. The units M_1, M_2, and M_3 produce bulbs in the proportions of 2:2:1, respectively. It is known that 20 \% of the bulbs produced in the factory are defective. It is also known that, of all the bulbs produced by M_1, 15 \% are defective. Suppose that, if a randomly chosen bulb produced in the factory is found to be defective, the probability that it was produced by M_2 is 2 5 . If a bulb is chosen randomly from the bulbs produced by M_3, then the probability that it is defective is ____.