NoGiven:
The length of each side is 16in.
To find:
The probability that a dart would land in the shaded region.
Explanation:
First, find the whole area.
[tex]\begin{gathered} A=a^2 \\ =16^2 \\ A=256\text{ square inches} \end{gathered}[/tex]
Next, find the area of the shaded region.
[tex]\begin{gathered} Shaded\text{ area = Whole area-unshaded area} \\ Area=Whole\text{ area-\lparen4}\times Area\text{ of the quadrant\rparen} \\ A=256-4\times\frac{\pi r^2}{4} \\ A=256-\pi r^2 \end{gathered}[/tex]
Substituting r = 8 we get,
[tex]\begin{gathered} A=256-3.14(8^2) \\ A=256-200.96 \\ A=55.04\text{ square inches} \end{gathered}[/tex]
The probability is,
[tex]\begin{gathered} P(E)=\frac{Area\text{ of the shaded region}}{Total\text{ area}} \\ =\frac{55.06}{256} \\ P(E)=\frac{43}{200} \\ (or) \\ =0.215 \end{gathered}[/tex]
Final answer:
The probability that a dart would land in the shaded region is,
[tex]\frac{43}{200}\text{ \lparen or\rparen 0.215}[/tex]
