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+18 votes
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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?

  1. $np(1-p)^{n-1}$

  2. $(1-p)^{n-1}$

  3. $p(1-p)^{n-1}$

  4. $1-(1-p)^{n-1}$

asked in Computer Networks by Veteran (69k points) | 1.9k views

$\text{(A) is correct option!}$

From which book ??

2 Answers

+26 votes
Best answer

Probability that only one station transmits in a given slot = ${n \choose 1} p^1 (1-p)^{n-1}$

answer = option A

$p$ for 1 transmitting and $(1-p)$ for $n-1$ non transmitting and $n$ ways to choose $1$ from $n$.

answered by Boss (5.1k points)
edited by
Can you explain it more ?
+6 votes
Please before making above question clear your concept about Binomial distribution,then this question will seem like birthday cake

Solotion::

P(X=1)=nC1 x (p)^1 x (1-p)^n-1
answered by Boss (8.4k points)


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