Answer
$\dfrac{2}{9}$ or, $22.2 \%$
Work Step by Step
The area of shaded region is equal to $\dfrac{80}{360}\times \pi (3)^2=2 \pi \ in.^2$
Total area $=\pi \times (3)^2=9 \pi \ in.^2$
Now, the probability that the point lies in the shaded region is the ratio of area of the shaded region to the total area:
P(area of shaded region)$=\dfrac{2 \pi}{9 \pi}=\dfrac{2}{9}$ or, $22.2 \%$
