[tex]\text{probability it would and on the white sector=}\frac{area\text{ of white sector}}{\text{area of the circle}}[/tex][tex]\begin{gathered} \text{area of the white sector=}\frac{\theta}{360}\times\pi\times r^2 \\ \theta=360-120=240\text{ degree} \\ r=9 \\ \text{area of the white sector=}\frac{240}{360}\times\pi\times9^2 \\ \text{area of the white sector=}\frac{2}{3}\times\pi\times81^{} \\ \text{area of the white sector=}\frac{162\pi}{360} \\ \text{area of the white sector=}\frac{27}{60}\pi=\frac{9}{20}\pi \end{gathered}[/tex][tex]\begin{gathered} \text{area of the circle=}\pi\times r^2 \\ \text{area of the circle=9}^2\times\pi \\ \text{area of the circle=81}\pi \end{gathered}[/tex][tex]\begin{gathered} \text{probability}=\frac{\frac{9}{20}\pi}{81\pi} \\ \text{probability it would land on the white sector=}\frac{9}{20}\pi\times\frac{1}{81\pi} \\ \text{probaility = }\frac{1}{20\times9}=\frac{1}{180} \end{gathered}[/tex]
To find the probability that the dart will land on the large white sector is by dividing the area of the white sector by the whole area of the circle. The area of the white sector is first calculated with the area of a sector formula where the angle is equals to 240 degree and the radius is 9. Then the area of the circle is calculated by using the area of a circle formular . The radius is 9 also.
