Final answer:
To calculate the probability that a coin will not touch any edges of any square on the checkerboard, we need to find the probability that the entire coin falls within a single square.
Step-by-step explanation:
To calculate the probability that a coin will not touch any edges of any square on the checkerboard, we need to find the probability that the entire coin falls within a single square.
To do this, we need to find the area of the square and the area of the circle.
Let's calculate the probabilities for each coin:
a. The diameter of a dime is 18 mm, so the radius is 9 mm. The area of the circle is pi times the square of the radius, which is 81 pi mm². The area of each square is 30 mm x 30 mm = 900 mm². The probability that the coin will not touch any edges is the area of the circle divided by the area of the square, which is (81 pi) / 900.
b. The diameter of a nickel is 24 mm, so the radius is 12 mm. The area of the circle is 144 pi mm². The probability is (144 pi) / 900.
c. The diameter of a quarter is 30 mm, so the radius is 15 mm. The area of the circle is 225 pi mm². The probability is (225 pi) / 900.