Question
If Sheldon randomly chooses a point in the square below, what is the probability that point is not in the
circle? Assume that pi = 3.14 and round to the nearest
tenth of a percent.
circle? Assume that pi = 3.14 and round to the nearest
tenth of a percent.
Answers
GPT 3.5
To find the probability that a randomly chosen point is not in the circle, we need to find the area of the circle and the area of the square.
The side length of the square is 8 units, so the area of the square is 8 * 8 = 64 square units.
The radius of the circle is half of the side length of the square, so the radius is 4 units. The area of the circle is pi * r^2 = 3.14 * 4^2 = 3.14 * 16 = 50.24 square units.
The probability that a randomly chosen point is not in the circle is the ratio of the area of the square that is not in the circle to the total area of the square:
Probability = (Area of square - Area of circle) / Area of square
Probability = (64 - 50.24) / 64
Probability = 13.76 / 64
Probability ≈ 0.2144
Probability ≈ 21.4%
So, the probability that a randomly chosen point is not in the circle is approximately 21.4%.
The side length of the square is 8 units, so the area of the square is 8 * 8 = 64 square units.
The radius of the circle is half of the side length of the square, so the radius is 4 units. The area of the circle is pi * r^2 = 3.14 * 4^2 = 3.14 * 16 = 50.24 square units.
The probability that a randomly chosen point is not in the circle is the ratio of the area of the square that is not in the circle to the total area of the square:
Probability = (Area of square - Area of circle) / Area of square
Probability = (64 - 50.24) / 64
Probability = 13.76 / 64
Probability ≈ 0.2144
Probability ≈ 21.4%
So, the probability that a randomly chosen point is not in the circle is approximately 21.4%.