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In this system, the reliability of each component is the complement of its failure probability. Given that the failure probability of each component is \(0.64\), the reliability (probability that each component works) is \(1 - 0.64 = 0.36\).

### Analyzing the Network:
The system has components arranged both in series and parallel. The reliability rules are:

1. **Series components**: If components are in series, all must work for the system to work. The overall reliability is the product of their individual reliabilities.
   
2. **Parallel components**: If components are in parallel, only one needs to work for the system to work. The overall reliability is \(1 - \text{(failure probability of all)}\).

### Step 1: Reliability of the two parallel branches
Each of the two branches between \(A\) and \(B\) consists of 2 components in series. The reliability of a series connection is:
\[
R_{\text{series}} = 0.36 \times 0.36 = 0.1296
\]
This applies to both branches.

### Step 2: Reliability of the entire system
Now, the two branches are in parallel. For parallel reliability:
\[
R_{\text{parallel}} = 1 - (1 - R_{\text{series}}) \times (1 - R_{\text{series}})
\]
Substituting \(R_{\text{series}} = 0.1296\):
\[
R_{\text{parallel}} = 1 - (1 - 0.1296) \times (1 - 0.1296)
= 1 - (0.8704 \times 0.8704)
= 1 - 0.75759536
= 0.24240464
\]

So, the system's reliability is approximately \(0.24240\).

### Final Answer:
The system's reliability is \(0.24240\), rounded to five decimal places.

Let me know if you'd like further details or if you have any questions. 

Here are some relative questions you might consider:
1. How does the reliability of a system change with more parallel components?
2. What happens to reliability if the failure probability increases?
3. How can reliability be improved in a series system?
4. How do different types of component arrangements (series vs. parallel) affect the overall reliability?
5. How would you calculate reliability if the system had three components in each branch?

**Tip**: When calculating parallel reliability, remember that it represents the probability that at least one component works.

In the system above, each component fails with probability 0.64 independently of other components. Compute the system’s reliability. Round your answer to five decimal places.

Learn how to compute the reliability of a system where each component has a failure probability of 0.64. The solution involves applying probability theory to both series and parallel arrangements of components. Suitable for undergraduate students in reliability engineering.

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