Question

Coin of radius is 3cm , probability coin will completely land in the square

Answer 1

The best way to look at the problem is to reformulate

The coin falls completely inside a single square.

to

The center of the coin is at least one coin radius from any grid line.

You can then shade the area of a grid square where the coin center cannot fall -- this shaded area will look the same in every square. If the coin radius is rr and the grid square sides have length dd, there's a small square of side length d−2r in each square where the center can fall without the coin extending beyond the grid square.

So the probablity of staying within the square becomes

(d−2r)^2/d^2assuming that the position of the coin's center relative to the square it happens to land on is uniformly distributed.