An industrial plant manufactures photovoltaic cells using three separate production lines: Alpha ($A$), Beta ($B$), and Gamma ($G$). The proportions of the total output produced by each line are 0.45, 0.30, and 0.25 respectively. Data shows that the probability of a cell being defective ($D$) from Line Alpha is 0.02, from Line Beta is 0.04, and from Line Gamma is 0.06.