In archery, targets are marked with 10 evenly spaced concentric rings, which have values 1 through 10 assigned to them. In addition, there is an inner 10 ring, sometimes called the X ring. This becomes the 10 ring at indoor compound competitions. Outdoor it serves as a tie breaker, with the archer scoring the most Xs winning. Suppose we have an outdoor competition using an olympic size target, which has a diameter of 12cm. When a particular archer shoots an arrow, it is equally likely to fall anywhere on the target, but it will hit the target.

Find the probability function of the score obtained from the archer shooting one arrow at the target.

I tried binomial but this didn't work

$\displaystyle \displaystyle p(x)=\binom{10}{x}\left(\frac{1}{10}\right)^x\left (\frac{9}{10}\right)^{10-x}$