Let $A_1 = (0, 0), A_2 = (1, 0), A_3 = (1, 1)\ $and$\ A_4 = (0, 1)$ be the four vertices of a square. A particle starts from the point $A_1$ at time $0$ and moves either to $A_2$ or to $A_4$ with equal probability. Similarly, in each of the subsequent steps, it randomly chooses one of its adjacent vertices and moves there. Let $T$ be the minimum number of steps required to cover all four vertices. The probability $P(T = 4)$ is
- $0$
- $1/16$
- $1/8$
- $1/4$