A graph consists of a collection of nodes the dots in the fi

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.)

Solution

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