MathDB

Consider a computer network consisting of servers and bi-directional communication channels among them. Unfortunately, not all channels operate. Each direction of each channel fails with probability

p

and operates otherwise. (All of these stochastic events are mutually independent, and

0 \le p \le 1

.) There is a root serve, denoted by

r

. We call the network operational, if all serves can reach

r

using only operating channels. Note that we do not require

r

to be able to reach any servers.
Show that the probability of the network to be operational does not depend on the choice of

r

. (In other words, for any two distinct root servers

r_1

and

r_2

, the operational probability is the same.)

Problem Statement