Given:
A rectangle with sides 40 and 25.
A circle with radius 8 inside the rectangle.
The area of circle is unshaded.
To find:
The probability that a point (randomly selected) will lie in the unshaded region.
Solution:
The area of the rectangle is:
[tex]A_1=Length\times Width[/tex]
[tex]A_1=40\times 25[/tex]
[tex]A_1=1000[/tex]
The area of the circle is:
[tex]A_2=\pi r^2[/tex]
Where, r is the radius.
[tex]A_2=\pi (8)^2[/tex]
[tex]A_2=\pi (64)[/tex]
[tex]A_2=64\pi[/tex]
[tex]A_2\approx 201.06[/tex]
The probability that a point (randomly selected) will lie in the unshaded region is:
[tex]\text{Probability}=\dfrac{\text{Unshaded region}}{\text{Total region}}[/tex]
[tex]\text{Probability}=\dfrac{A_2}{A_1}[/tex]
[tex]\text{Probability}=\dfrac{201.06}{1000}[/tex]
[tex]\text{Probability}=0.20106[/tex]
Therefore, the required probability is 0.20106.
