10. If in the quadratic equation $x^{2}-2(a-3) x-b^{2}+9=0$, $a$ and $b$ are the numbers obtained by rolling a die, then the probability $P=(\quad)$ that the quadratic equation has two positive roots is:
A. $\frac{1}{18}$
B. $\frac{1}{9}$
C. $\frac{1}{6}$
D. $\frac{13}{18}$
10. A. From the quadratic equation having two positive roots, we know $\left\{\begin{array}{l}\Delta \geqslant 0, \\ a-3>0, \\ -b^{2}+9>0 .\end{array}\right.$ Solving this, we get $\left\{\begin{array}{l}a=6, \\ b=1\end{array}\right.$ or $\left\{\begin{array}{l}a=6, \\ b=2 .\end{array}\right.$ Therefore, $P=\frac{2}{36}=\frac{1}{18}$.