In a high-precision manufacturing facility, the probabilities of three distinct system faults—Mechanical ($M$), Electrical ($E$), and Software ($S$)—occurring during a single operation are monitored. It is known that Mechanical and Software faults are mutually exclusive events ($M\cap S=\varnothing$). The following probabilities are recorded:

$$P(M\cap E^{\prime })=\frac{7}{50}$$ $$P(M\cap E)=0.035$$ $$P(E\cap M^{\prime }\cap S^{\prime })=0.245$$ $$P(E\cap S)=\frac{3}{20}$$ $$P(S\cap E^{\prime })=0.38$$

The probability that an operation completes without any of these three faults occurring is denoted by $\lambda$. Determine the value of $\lambda$.