Please solve 3 and 4

Figure I.2. Layout options for the main network (each node represents a local network). The network is "up" if there is at least one path connecting each pair of (local) nodes in the network. So, we need both the reliability of each local network and the reliability of the interregional cables (denoted by q ) to calculate the system reliability of the full network. Questions about local network reliability Hint: it is convenient to use the built-in functions of EXCEL for your calculations, for example the binominal distribution: BINOMDIST(number_s,trials,probability_s,cumulative); see the EXCEL help function for details. Question 1. What do the layout options 3A,4A,5A and 6A for the local networks (Figure I.I) have in common? Calculate the reliability for these local networks in a spreadsheet for p=0.9,0.95 and 0.99 . Question 2. What do the layout options 3B, 4B, 5B and 6B for the local networks (Figure I.I) have in common? Calculate the reliability for these local networks in a spreadsheet for p=0.9,0.95 and 0.99 . Question 3. Give the minimal path vectors and minimal cut vectors for layout option 4C (Figure I.I). Explain how the system reliability can be calculated using these minimal path vectors and minimal cut vectors (you do not have to make calculations by now). Question 4. Explain how pivotal decomposition can be used to calculate the reliability of local network 4C (Figure I.I). Question 5. Add formulas for the reliability of local network 4C (Figure I.1) to your spreadsheet. Calculate the reliability for p=0.9,0.95 and 0.99 . Check your own work: the reliability of local network 4C should be around 0.977 if p=0.90 Question 6. Derive formulas for the reliability of the rest of the local networks (Figure I.I). Add these formulas to your spreadsheet and calculate the reliability of each local network type for p=0.9,0.95 and 0.99 . Questions about the overall network reliability Question 7. Calculate in your spreadsheet the system reliability for each of the five overall network layouts (Figure I.2), assuming for the time being that all local networks are 100% reliable and that the interregional connection reliability equals q=0.99