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Consider a random graph with n nodes. Each pair of nodes (a tuple) can be connected with an edge with probability p. For arbitrary nodes: (1, b, c, d in the graph, the event a, b are connected is independent of the event c, d are connected. You can imagine the graph to be a social network with n people, in which each pair of people can be friends at random. The event of being friends is independent of other pairs of people being friends. Given n = 7,1) = % Use the union bound to give an upper bound of the event in which there exists a node that is not connected with any other node