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A graph is constructed iteratively according to the following algorithm. The graph starts as a single vertex. With probability p, the graph stops here. Otherwise, 3 new
vertices are constructed and joined to this vertex. If we have a graph with more than one vertex, for each vertex created at the previous stage, 3 new vertices are construed and joined to it with probability 1−p. We repeat this
process until no new vertices are added. When the expected number of vertices in this graph is 100, the value
of p can be expressed as a/b
where
a and
b are coprime
positive integers. What is the value of a+b

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