Question

There are n stations in a 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?

a) np(1-p)^(n-1)
b)(1-p)^(n-1)
c)p(1-p)^(n-1)
d)1-(1-p)^(n-1)

Answer 1

The experiment can be described using Bernoulli trial.

Let's consider the event of transmitting the station as "success".

Then probability that only one station transmits in a given time slot equals to

$$\binom {n} {1} p ^ {1} (1 - p) ^ {n - 1} = n p (1 - p) ^ {n - 1}$$

ANSWER: A