Question 1109026
{{{drawing(300,300,-3.2,3.2,-3.2,3.2,
circle(0,0,0.05),circle(0,0,1),circle(0,0,3),
red(arrow(-1,0,1,0)),red(arrow(1,0,-1,0)),
red(arrow(0,1.5,0,0)),red(arrow(0,1.5,0,3)),
locate(0.3,0,1in),locate(0.1,1.7,1.5in)
)}}}
As the diameter of the outer bullseye circle is {{{3}}} times the diameter of the inner bullseye small circle,
the area of the outer bullseye is {{{3^2=9}}} times the area of the inner bullseye.
Similarly, as the diameter of the dartboard is {{{18}}} times the diameter of the inner bullseye,
the area of the dartboard {{{18^2=324}}} times the area of the inner bullseye.
If every location on the board is equally likely to be hit by the dart,
on average, out of every {{{324}}} darts hitting the dartboard,
{{{1}}} dart that hits the 1-in diameter inner bullseye,
{{{9-1=8}}} darts miss the nner bullseye, but land inside the outer bull.
So, the probability that a dart thrown at the board misses the inner bullesye but lands inside the outer bull is
{{{8/324}}}{{{"="}}}{{{highlight(2/81)}}} .