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 \( \dfrac{2}{5} \).
If a bulb is chosen randomly from the bulbs produced by \( M_3 \), then the probability that it is defective is ___________.
