A graph consists of a collection of nodes (the dots in the figure) connected by

Question

A graph consists of a collection of nodes (the dots in the figure) connected by edges (line segments from one node to another). A move on a graph is a move from one node to another along a single edge. Find the probability of going from Start to Finish in a sequence of two random moves in the graph shown. (All directions are equally likely.)

A graph consists of a collection of nodes (the dots in the figure) connected by edges (line segments from one node to another). A move on a graph is a move from one node to another along a single edge. Find the probability of going from Start to Finish in a sequence of two random moves in the graph shown. (All directions are equally likely.)

Explanation / Answer

From start to finish there are two paths which can lead to finish in two steps

P( in two random steps) = P( first step towards finish)*P(next step to finish)

                                  = (1/4)*(1/4) +(1/4)*(1/4) =1/8 = 0.125

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