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Official PYQ · 2007Q65Data Link Layer: Framing, Error Detection, MAC, Ethernet BridgingMCQ1 mark

GATE CS 2007 Q65 — Data Link Layer: Framing, Error Detection, MAC, Ethernet Bridging

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There are nn stations in slotted LAN. Each station attempts to transmit with a probability pp in each time slot. What is the probability that ONLY one station transmits in a given time slot?

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Answer: A

To find the probability that only one station transmits in a given time slot, we can model the transmission attempts of the nn stations as independent Bernoulli trials.

For any given time slot:

  • The probability that a specific station attempts to transmit is pp.
  • The probability that a specific station does not attempt to transmit is 1−p1 - p.

For exactly one station to transmit, we must choose 11 station out of the nn available stations to transmit, while the remaining n−1n - 1 stations do not transmit.

Using the binomial probability formula:

P(Exactly 1 station transmits)=(n1)⋅p1⋅(1−p)n−1P(\text{Exactly } 1 \text{ station transmits}) = \binom{n}{1} \cdot p^1 \cdot (1 - p)^{n-1}

Simplifying this expression:

P(Exactly 1 station transmits)=np(1−p)n−1P(\text{Exactly } 1 \text{ station transmits}) = n p (1 - p)^{n-1}

Therefore, the correct option is A.

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