Consider a communication network with four nodes n1, n2, n3 and n4 and five directed links l1 = (n1, n2), l2 = (n1, n3), l3 = (n2, n3), l4 = (n3, n2), l5 = (n2, n4) and l6 = (n3, n4). A message has to...

Consider a communication network with four nodes n1, n2, n3 and n4 and five directed
links l1 = (n1, n2), l2 = (n1, n3), l3 = (n2, n3), l4 = (n3, n2), l5 = (n2, n4) and l6 = (n3, n4). A
message has to be sent from the source node n1 to the destination node n4. The network is
unreliable. The probability that the link li is functioning is pi for i = 1, . . . , 5. The links behave
physically independent of each other. A path from node n1 to node n4 is only functioning if
each of its links is functioning. Use the inclusion-exclusion formula to find the probability that
there is some functioning path from node n1 to node n4. How does the expression for this
probability simplify when pi = p for all i?