There are n stations in a slotted LAN. Each station attempts to transmit with…
2024
There are n stations in a slotted LAN. Each station attempts to transmit with a probability p in each time slot. What is the probability that only one station transmits in a given time slot?
- A.
1 − (1 − p)ⁿ⁻¹
- B.
(1 − p)ⁿ⁻¹
- C.
n × p × (1 − p)ⁿ⁻¹
- D.
p × (1 − p)ⁿ⁻¹
- E.
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Correct answer: C
This problem is based on probability in a Slotted ALOHA-like system.
There are n stations
Each station transmits with probability p
We want the probability that exactly one station transmits
Step-by-step logic:
Choose 1 station out of n → n ways
That chosen station transmits → probability = p
Remaining (n − 1) stations do NOT transmit → probability = (1 − p)^{n−1}
Multiply all:
P=n⋅p⋅(1−p)n−1