Consider a large Erdos-Renyi random network. Let S denote the fraction of nodes within the largest component. (a) What is the probability that a node with degree k is not in the largest component? (b) Let C denote the set of nodes in the largest component. Let i be a node in the network. Find the probability P(ki=ki/C) that a node has degree k given that the node is not part of the largest component. (Hint: Bayes' Theorem may be useful here: P(AB)=P(BA)P(A)/P(B) )