Question

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 the tile? In other words, the coin should not cross the edge of any tile.

Answer 1

Answer:

Side of the red square = 10 - (3+3) = 4

Area of the red square = 4*4 = 16

Area of a tile (black square) = 10*10 = 100

Required probability = 16/100 = 4/25

Answer 2

The probability that the coin will land completely within the tile is 0.16

Step-by-step explanation:

A coin of radius 3 cm is randomly dropped on a square floor full of square shaped tiles of side 10 cm each

side of the square tile = 10 cm

radius of the coin = 3 cm

center of the coin should lie in the square region having area=

( side of the square tile - 2×radius of the coin)²

= (10- 2×3)²

= (10- 6)²

= (4)²= 16

as the tiles are in the shape of the square

therefore

total area of the tile = (side)²

total area of the tile = (10)² = 100

then, the probability that the coin should not cross the edge of any tile

= $\frac{16}{100}$

= 0.16

hence , the probability that the coin will land completely within the tile is 0.16

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