Answer: \(P=\frac{1}{16}\)
Step-by-step explanation:
In the given picture, the the radius of the shaded region = 3 inches
The area of the shaded region =\(\pi r^2=3.14\times(3)^2=3.14\times9\)
Thus, The area of the shaded region =28.26 square inches
Radius of whole figure = 12 inches
The area of whole figure= \(\pi r^2=3.14\times(12)^2=3.14\times144\)
Thus, The area of the whole figure=452.16 square inches
Now, the probability that it will land in the shaded region is given by :-
\(P=\frac{\text{area of shaded region}}{\text{area of the whole figure}}\\\\\Rightarrow\ P=\frac{28.26}{452.16 }\\\\\Rightarrow\ P=\frac{1}{16}\)
