Question: =+17. Consider a random graph with n nodes. Between every pair of nodes, independently introduce an edge with probability p. If c(p) denotes the probability

=+17. Consider a random graph with n nodes. Between every pair of nodes, independently introduce an edge with probability p. If c(p) denotes the probability that the graph is connected, then it is intuitively clear that c(p) is increasing in p. Give a coupling proof of this fact.

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