ITPEC FE Subject A October 2025 Question 12
One (1) server, three (3) clients, and two (2) printers are connected via a LAN as shown in the figure below. This system prints data that is located on the server in response to instructions from the clients. When the availability of each device is as shown in the table below, which of the following is the expression that represents the availability for the system? Here, the system is considered available if one (1) of the three (3) clients and one (1) of the two (2) printers are running.
Explanation
a(1 − (1 − b)³)(1 − (1 − c)²) — the server is in series with a parallel group of clients and a parallel group of printers.
- •The server has no backup, so it contributes a
- •The clients fail as a group only if all three fail, with probability (1 − b)3, so the group's availability is 1 − (1 − b)3
- •The printers likewise: 1 − (1 − c)2
- •The LAN is 1, and all three parts must work, so multiply: a(1 − (1 − b)3)(1 − (1 − c)2)
Answer (d)
Why not others:
- •(a) — ab3c2 requires every client and every printer to run, a pure series system
- •(b) — 1 − b3 is the probability that not all three clients run, not that at least one does
- •(c) — (1 − b)3(1 − c)2 is the probability that every client and every printer is down
Key rule: In series, multiply availabilities; for "at least one of n" in parallel, use 1 − (1 − x)n, one minus the chance that all fail.
System Component · AI-written, may contain errors
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