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?
$np(1-p)^{n-1}$
$(1-p)^{n-1}$
$p(1-p)^{n-1}$
$1-(1-p)^{n-1}$
$\text{(A) is correct option!}$
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 $n$.
Gatecse