GATE CSE 2007 | Question: 65

Question

There are $n$ stations in 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. $np(1-p)^{n-1}$

• B. $(1-p)^{n-1}$

• C. $p(1-p)^{n-1}$

• D. $1-(1-p)^{n-1}$

Comments

Application of this question: https://gateoverflow.in/3729/gate2004-it-85

---

Book : Computer Networking - Kurose : Ross 7th Global edition

Page : 485

---

GO to the Root of Concept: Video Explanation with timestamp: Derivation Efficiency & Throughput of Aloha | In-Depth | GATE 2021, 2004, 2007 PYQs | With NOTES

Answer 1

Out of all stations only 1 allowed to transmit so to select  1 station out of N stations there are N ways possible (ⁿC₁ ) then 
it must transmit and other n-1 stations should not transmit 
therefore    n * p * (1-p)*(1-p)*.............(1-p)
= np(1-p)^n-1

Answer 2

as u can do it with the help of  probability distribution

n is the no of station out of  which 1 sation send the data then the probability of transmitting of1 station is (p)^1

and the probabilty of transmitting "n-1" staion is (1-p)^n-1 which is unsuccess probability then u got the answer.

Answer 3

Event 1: Only one station should transmit

We can select one station out of 1 station in C(n,1 ) ways = n

This station has to transmit with the probability 'p'

Therefore, P(E1) = n * p

Event 2: Remaining (n-1) stations should not transmit

Then remaining (n-1) stations should not transmit.

So, for all of them probability will be (1-P)

therefore, P(E2) = (1-p)^(n-1).

Now, both the events should occur simultaneously

Hence, n * p * (1 - p )^(n-1)