Find the area of small and large circles:
[tex] A_{small}=\pi r_1^2=\pi \cdot (8.01)^2=64.1601,\\
A_{large}=\pi r_2^2=\pi \cdot (4.02)^2=16.1604 [/tex].
The area of the shaded region is
[tex] A_{shaded}=A_{large}-A_{small}=64.1601-16.1604=47.9997 [/tex].
Use the geometric probability to determine the probability that randomly selected point will be in the shaded region:
[tex] Pr=\dfrac{A_{shaded}}{A_{large}} =\dfrac{47.9997}{64.1601} =0.7481 [/tex].
In percent 0.7481 is 74.81% and rounded to the nearest tenth is 74.8%.
Answer: 74.8%.
