Let P be a point in a plane with a coordinate system that is initially located at the origin $(0,0)$ and moves in the plane according to the following rule:
One dice is thrown. When the number on the dice is a multiple of three, point P moves 1 unit in the positive direction of the $x$-axis, and when the number on the dice is not a multiple of three, point P moves 1 unit in the positive direction of the $y$-axis.
Assume that the dice is thrown four times.
(1) The probability that P reaches point $(3,1)$ is $\frac{\mathbf{A}}{\mathbf{BC}}$.
(2) Altogether, the number of the points which P can reach is $\mathbf{D}$, and the coordinates of these points can be expressed in terms of an integer $k$ as
$$(k,\, \mathbf{E} - k) \quad (\mathbf{F} \leq k \leq \mathbf{G}).$$
Let us denote the probability that P can reach a given point $(k, \mathbf{E} - k)$ by $p_k$. Then the maximum value of $p_k$ is $\frac{\mathbf{HI}}{\mathbf{HI}}$, and the minimum value of $p_k$ is $\frac{\mathbf{J}}{\mathbf{BC}}$.
(3) The probability that $P$ passes through point $(1,1)$ and reaches point $(2,2)$ is $\frac{\mathbf{KL}}{\mathbf{BC}}$.