Answer
See the detailed answer below.
Work Step by Step
$$\color{blue}{\bf [a]}$$
We cannot be sure about the wall if it is charged or not.
If the rubber ball is rubbed with wool, the rubber ball will acquire a negative charge since it gains electrons from the wool.
Now we know that the ball is carrying a negative charge, and hence the wall will attract the ball in two cases. First, if it is carrying a positive charge since unlike charges attract. Second, if it is neutral and we approach the ball to the wall (preventing it from touching it), then the side that faces the ball will be polarized since the negative charge will repel and move away from the ball to the other side.
Now the side that faces the ball is polarized, and we can say it is positively charged, so it will attract the negatively charged rubber ball. Therefore, when we release the ball, it will stick to the wall.
Now, the two forces, the repulsive force from the negative side of the wall acting leftward, and the attractive force from the positive side of the ball acting rightward, are equal in magnitude and opposite in direction, as shown in the figure below.
But what prevents it from sliding down? In this situation, there are two vertical forces exerted on the ball: the static friction force from the wall, which acts upward, and the ball's weight, which acts downward.
These two forces are equal in magnitude and opposite in direction.
$$\color{blue}{\bf [b]}$$
