A coin of radius 3 cm is randomly dropped on a square floor full of square shaped tiles of side 10 cm each. What is the probability that the coin will land completely within a tile? In other words, the coin should not cross the edge of any tile.

The radius of the coin is 3 cm. 
So, if the coin should not cross the edge, the centre of the coin should at least be 3 cm away from the edge of the tile. 

In the given diagram the center of the circle should lie in the blue region. As we can see, the area in which the centre of the coin can fall is a square of side 10-3-3 = 4 cm. 
Therefore, the area in which the centre of the coin can fall is 16 square cm. 
Area of the tile = 100 square cm.
Required probability = 16/100 = 0.16.
Therefore, option E is the right answer.