Question:
Transmission of information between computers s and t (see figure) is possible if there is at least one closed path between s and t. The figure indicates the possible interruption of an edge (connection between two nodes of the transmission graph) by a switch. In practice, such an interruption may be caused by a cable break or if the transmission capacity of a channel is exceeded. All 5 switches operate independently. Each one is closed with probability p and open with probability 1 - p. Only switch 3 allows for transmitting information into both directions.
(1) What is the probability that ws,t(p) s can send information to t?
(2) Draw the graph of as a function of w p, 0 ≤ p ≤ 1