Consider a square ABCD with a line joining B to D. This forms a bi-directional graph G with vertices at A, B,C and D.

Consider a point particle performing a random walk on this graph. At each stage, the particle moves to a neighbour of its existing vertex. It chooses 1 such possible neighbor at each stage with equal probability.

If the particle starts at A, what's the expected number of steps until it reaches A again? Round to the nearest 0.01

Pick ONE option

5.00

3.00

2.66

6.20