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 $\frac { 2 } { 5 }$.
If a bulb is chosen randomly from the bulbs produced by $M _ { 3 }$, then the probability that it is defective is $\_\_\_\_$.