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 $P=$ ( ) that the quadratic equation has two positive roots.
(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 $\left\{\begin{array}{l}\Delta \geqslant 0, \\ a-3>0, \\ -b^{2}+9>0 \text {. }\end{array}\right.$
Solving, we get $a=6, b=1$ or $a=6, b=2$.
Thus, $P=\frac{2}{36}=\frac{1}{18}$.