In a high-precision manufacturing facility, the probabilities of three distinct system faults—Mechanical (MMM), Electrical (EEE), and Software (SSS)—occurring during a single operation are monitored. It is known that Mechanical and Software faults are mutually exclusive events (M∩S=∅M \cap S = \emptysetM∩S=∅). The following probabilities are recorded:
P(M∩E′)=750 P(M \cap E') = \frac{7}{50} P(M∩E′)=507 P(M∩E)=0.035 P(M \cap E) = 0.035 P(M∩E)=0.035 P(E∩M′∩S′)=0.245 P(E \cap M' \cap S') = 0.245 P(E∩M′∩S′)=0.245 P(E∩S)=320 P(E \cap S) = \frac{3}{20} P(E∩S)=203 P(S∩E′)=0.38 P(S \cap E') = 0.38 P(S∩E′)=0.38The probability that an operation completes without any of these three faults occurring is denoted by λ\lambdaλ. Determine the value of λ\lambdaλ.
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.