A manufactured device has exactly one of three mutually exclusive fault types: electrical, mechanical or other. Their probabilities are xxx, 2x 2x\,2x and 1−3x1-3x1−3x respectively. In a batch of 200 devices, the expected number with an electrical fault is 48.
Find the probability of each fault type.
Two devices are selected independently. Find the probability that they have the same fault type.
Find the probability that at least one of the two devices has an electrical fault.
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.