13,786 views
32 votes
32 votes

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

7 Answers

Best answer
48 votes
48 votes

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

Answer is option A.

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

edited by
14 votes
14 votes

Let the stations be $S_1, S_2, S_3,...,S_n $

 

The probability that only one station transmits is:-

Either $S_1$ transmits and no other transmits

Or, $S_2$ transmits and no other transmits

Or, $S_3$ transmits and no other transmits

so on.

 

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

=> $np(1-p)^{n-1}$

 

Option A

12 votes
12 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
2 votes
2 votes
There are "n" stations in LAN. According to question, only one station want to transmit , in the sense among "n" stations, "n-1" should not be allowed to transmit the data  when one station is already is tranmitting the data.

In our question suppose "n" leveled station is transmitting the data with probability "p" then remaining '"n-1" should not be allowed to transmit the data at given slot.

So, np.(1-p)^ n-1.

(B)
Answer:

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