[tex]P(\text{Event)}=\frac{n\text{ (Event)}}{Total\text{ Event}}[/tex][tex]P(\text{outer most ring)=}\frac{area\text{ of the outer most ring}}{area\text{ of the dartboard}}[/tex][tex]\begin{gathered} Area\text{ of the dartboard=}\pi\times R^2 \\ Where\text{ R=6} \\ \text{Area of the dartboard=}\pi\times6^2 \\ \text{Area of the dartboard=}36\pi \end{gathered}[/tex][tex]\begin{gathered} \text{Area of the outermost ring=Area of the dartboard - Area of the inner ring} \\ \text{Area of the outermost ring=36}\pi-(\pi\times4^2)=36\pi-16\pi=20\pi \end{gathered}[/tex][tex]\begin{gathered} P(\text{outermost ring)=}\frac{20\pi}{36\pi} \\ P(\text{outermost ring)=}\frac{5}{9} \end{gathered}[/tex]
The probability of the outermost ring is 55.6%
