The shaded area is a sector. Find the area of whole circle and sector:
[tex] A_{circle}=\pi r^2,\\
A_{sector}=\dfrac{r^2\alpha}{2} =\dfrac{r^2\cdot \frac{106\pi}{180}}{2} =\dfrac{53\pi r^2}{180} [/tex].
Use the geometric probability to find the probability that point will be at the shaded region:
[tex] Pr=\dfrac{A_{shaded}}{A_{circle}} =\dfrac{\frac{53\pi r^2}{180} }{\pi r^2}=\dfrac{53}{180}=0.2944 [/tex].
In percent 0.2944 is 29.44% that is 29.4% rounded to the nearest tenth.
Answer: 29.4%
