Discussion
A system consists of 4 components, 3 of which form a parallel subsystem connected in series with the 4th component. The components work independently of each other. If the reliability of each component is 0.8, then the system reliability is :
Answer: D
The system reliability is 0.7936.
The parallel block of three components fails only if all three fail, and it is in series with the fourth component:
\[ \begin{aligned} R_{\text{parallel}} &= 1 - (0.2)^{3} = 0.992 \\ R &= 0.992 \times 0.8 = 0.7936 \end{aligned} \]
0.4096 is \(0.8^{4}\), all four components in series. The other values do not follow from this structure.
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