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

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+16

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

0
From which book ??

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

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

edited
0
Can you explain it more ?
+1
Binomial distribution with parameter (n,p)
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

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