Answer: The correct option is (C) 20%.
Step-by-step explanation: Given that a circle is inscribed in a square and a point in the figure is selected at random.
We are to find the probability that the point will lie in the part that is NOT shaded.
Let a units be the side length of the square.
Then, the area of the square will be
[tex]A_s=a^2.[/tex]
Also, the radius of the circle is equal to the half of the side length of the square. So, the area of the circle will be
[tex]A_c=\pi \left(\dfrac{a}{2}\right)^2=\dfrac{22}{7}\times\dfrac{a^2}{4}=\dfrac{11}{14}a^2.[/tex]
So, the area of the part that is not shaded is given by
[tex]A_{ns}=A_s-A_c=a^2-\dfrac{11}{14}a^2=\dfrac{3}{14}a^2.[/tex]
Therefore, the probability that the selected point is not in the shaded part is given by
[tex]p=\dfrac{A_{ns}}{A_s}\times100\%=\dfrac{\frac{3}{14}a^2}{a^2}\times100\%=\dfrac{300}{14}\%=21.42\%(approx.)[/tex]
Thus, the required probability is 20%.
Option (C) is CORRECT.
