An industrial plant manufactures photovoltaic cells using three separate production lines: Alpha (AAA), Beta (BBB), and Gamma (GGG). 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 (DDD) from Line Alpha is 0.02, from Line Beta is 0.04, and from Line Gamma is 0.06.
Construct a tree diagram to represent the production process and the associated defect probabilities.
Calculate the probability that a randomly selected cell: (i) was produced by Line Gamma and is defective, (ii) is not defective.
A quality control inspector finds a defective cell. Determine the probability that this cell was not produced by Line Alpha.