UGC NET CSE | January 2017 | Part 3 | Question: 25

Question

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. $n^P (1-P)^{n-1}$

Answer 1

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

Option 3