Skip to content
Related Articles

Related Articles

Improve Article

UGC-NET | UGC NET CS 2017 Jan – III | Question 25

  • Last Updated : 05 Apr, 2018
Geek Week

Suppose there are n stations in a slotted LAN. Each station attempts to transmit with a probability P in each time slot. The probability that only one station transmits in a given slot is _______.
(A) nP(1 – P)n – 1
(B) nP
(C) P(1 – P)n – 1
(D) nP(1 – P)n – 1


Answer: (A)

Explanation: P(X) = Probability that station X attempts to transmit = P
P(~X) = Probability that station X does not transmit = 1-P

Probability that only one station transmits = y
Y = (A1, ~A2, ~A3...~An) + (~A1, A2, ~A3....~An) + (~A1, ~A2, A3.....~An) + ..........+ (~A1, ~A2, ~A3....An)
  = (p * (1 - p) * (1 - p) * .....(1 - p) ) + ((1 - p) * p * (1 - p)......(1 - p) + ………….
  = p * (1 - p)(n-1) + p * (1 - p)(n - 1) + ……………………………………………. + p *(1 - p) ^ (n-1) 
  = n * p * (1 - p)(n - 1).

So, option (A) is correct.

Quiz of this Question

My Personal Notes arrow_drop_up
Recommended Articles
Page :