Wendy throws a dart at this square-shaped target:
A square is shown with sides labeled 10. A shaded circle is shown in the center of the square. The diameter of the circle is 2.
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:
To calculate the probability of hitting the black circle inside the target, we need to find the area of the circle and divide it by the total area of the square.
The radius of the circle is half of the diameter, so the radius is 2/2 = 1.
The area of the circle is πr^2 = π(1)^2 = π.
The area of the square is side^2 = 10^2 = 100.
Therefore, the probability of hitting the black circle is π/100, which is closer to 0. This is because the area of the circle is very small compared to the area of the square.
Part B:
To calculate the probability of hitting the white portion of the target, we need to find the area of the white portion and divide it by the total area of the square.
The area of the white portion is the area of the square minus the area of the circle. So, it is 100 - π.
The probability of hitting the white portion is (100 - π)/100, which is also closer to 0. This is because the white portion is still much smaller than the entire square.