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.
368 exam-style questions on Edexcel A Level Maths Conditional Probability, covering 2.1 Set Notation, 2.2 Conditional Probability, 2.3 Conditional Probabilities in Venn Diagrams, 2.4 Probability Formulae, and 2.5 Tree Diagrams. Each one has a worked solution and a mark scheme showing where the marks go.