Answer:
a)0.04
b)0.36
Explanation:
The probability of you randomly hitting the dart of a portion of the target would be the ratio of the area of the portion over the total area of the target.
Knowing that radius r = 10 in, the total area of the target is
[tex]A = \pi r^2 = \pi 10^2 = 100 \pi in^2[/tex]
a)The area of the portion that is 2 inches from the center
[tex]A_2 = \pi 2^2 = 4 \pi[/tex]
The chance of the dart hitting within 2 inches of the center is
[tex]P_2 = \frac{A_2}{A} = \frac{4\pi}{100\pi} = 1/25 = 0.04[/tex]
b) the area of the portion that is 2 inches from the rim is the total area of the target subtracted by the area of the 8 in radius circle
[tex]A_8 = A - \pi 8^2 = 100 \pi - 64 \pi = 36 \pi[/tex]
The chance of the dart hitting within 2 inches from the rim is
[tex]P_8 = \frac{A_8}{A} = \frac{36\pi}{100\pi} = 9/25 = 0.36[/tex]
