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.
200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.