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Question: Sophia throws a dart at this square-shaped target: A square is shown with sides labeled 9. A shaded circle is shown in the center of the square. The diameter of the circle is 3. 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) 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)
Part A: The probability of hitting the black circle inside the target is closer to 1. The area of the black circle is equal to πr2 = 3.14 x 32 = 28.26 square units. The area of the entire square is 9 x 9 = 81 square units. The fraction of the area of the black circle to the entire square is 28.26/81 = 0.35, which is closer to 1. Part B: The probability of hitting the white portion of the target is closer to 0. The area of the white portion is the area of the entire square (81 square units) minus the area of the black circle (28.26 square units). The area of the white portion is 81 - 28.26 = 52.74 square units. The fraction of the area of the white portion to the entire square is 52.74/81 = 0.65, which is closer to 0.
March 7, 2023, 5:02 p.m.
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