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.
Practise AQA A Level Maths 1.1 OT1: Mathematical argument, language and proof with exam-style questions for A Level Maths. 8 questions covering 1.1.1 Constructing mathematical arguments, 1.1.2 Mathematical language and syntax, 1.1.3 Set theory language and symbols, 1.1.4 Definition, domain and range of functions, and 1.1.5 Comprehending and critiquing arguments, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
