The probability of hitting the black circle is closer to 0. Therefore, the probability of hitting the target is closer to 0.

Part A: Is the probability of hitting the black circle inside the target closer to 0 or 1? Explain your answer and show your work. (5 points) To find the probability, we first need to find the areas of the square target and the shaded circle. The area of the square target (A_square) is given by the formula A = side^2. In this case, the side of the square is 9, so: A_square = 9^2 = 81 square units The area of the shaded circle (A_circle) is given by the formula A = π * r^2. The diameter of the circle is 3, so the radius (r) is half of that, which is 1.5. Therefore: A_circle = π * (1.5^2) = 2.25π ≈ 7.069 square units Now, we can find the probability of hitting the black circle inside the target (P_circle) by dividing the area of the circle by the area of the square: P_circle = A_circle / A_square ≈ 7.069 / 81 ≈ 0.087 Since 0.087 is closer to 0 than 1, the probability of hitting the black circle inside the target is closer to 0. Part B: Is the probability of hitting the white portion of the target closer to 0 or 1? Explain your answer and show your work. (5 points) We can find the probability of hitting the white portion of the target (P_white) by subtracting the probability of hitting the black circle from 1 (since the sum of the probabilities of hitting any spot within the square will always be 1). P_white = 1 - P_circle = 1 - 0.087 ≈ 0.913 Since 0.913 is closer to 1 than 0, the probability of hitting the white portion of the target is closer to 1.

Part A: The probability of hitting the black circle inside the target is closer to 1. This is because the area of the black circle is 9π, while the area of the square is 81. Therefore, the probability of hitting the black circle is (9π/81) = (3/9), which is closer to 1. Part B: The probability of hitting the white portion of the target is closer to 0. This is because the area of the white portion of the square is 72 (81-9π), while the area of the circle is 9π. Therefore, the probability of hitting the white portion of the target is (72/81), which is closer to 0.