3. Two towns are connected by a network of communication channels as shown in the following gure, in which -||- denotes a communication channel. The probability of a channel's failure-free operation or its reliability is R, and channel failures are independent. Minimal level of communication between towns can be guaranteed provided at least one path containing properly functioning channels exist. a) Derive an expression to determine the probability that the two towns will be able to communicate. Show all the steps Compose the reliability of smallest sub-paths comprising of individual channels, and then moving on to larger sub-paths. b) Plot this probability as a function of the reliability of an individual channel. What do you observe? Please use a tool such as Excel to plot your graphs. The graphs should be complete with labeled axis, legend, etc. 1 2 {at L | | 7