There are n stations in a slotted LAN. Each station attempts to transmit with…
2007
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-p)(n-1)
- B.
np(1-p)(n-1)
- C.
p(1-p)(n-1)
- D.
1-(1-p)(n-1)
Attempted by 376 students.
Show answer & explanation
Correct answer: B
Derivation and final answer:
Choose which station is the sole transmitter: there are n possible choices.
The chosen station transmits with probability p.
Each of the other n-1 stations must be silent, with probability (1-p) each, giving (1-p)^(n-1).
Multiply these factors to get the probability of exactly one transmission:
n * p * (1-p)^(n-1)
Therefore, the probability that only one station transmits in a given time slot is n p (1-p)^(n-1).