sir,please give me the sol

 

Refer to this figure to understand the answer of the problem.

 

The black area corresponds to the area in which the center of the coin cannot lie. The center of coin cannot lie on either side of the line till a distance of 1/3 inches as otherwise the line will be crossed.

Also since there is a vertical rim like carrom board so the center cannot lie within 1/3 inch from the boundary.

 

So we now calculate the area in which center can lie ..

 

This area comes out to be 3*(2-2/3)*3*(2-2/3) = 16.

 

Now the area in which the center can lie for all possible cases is (6-2/3)*(6-2/3)

 

Note that the area near the walls is not included because the center cannot lie within 1/3 inches of the walls.

 

Thus the probability that the lines will not be touched is

                                         

                                           16 / (6-2/3)*(6-2/3) = 0.5625

 

cheers