3. Nine small balls numbered $1, 2, \cdots, 9$ are placed in a bag. These balls are identical except for their numbers. Person A draws a ball from the bag, with the number being $a$, and then returns it. Person B then draws a ball from the bag, with the number being $b$. The probability that the inequality $a-2b+10>0$ holds is
A. $\frac{52}{81}$
B. $\frac{59}{81}$
C. $\frac{60}{81}$
D. $\frac{61}{81}$
Answer

As shown in the figure, there are 81 pairs of $(a, b)$ that satisfy the inequality $a-2b+10 \leqslant 0$. The number of $(a, b)$ pairs that satisfy this inequality is $2+4+6+8=20$. Let $A=$ “the inequality $a-2b+10>0$ holds”, then $P(A)=1-P(\bar{A})=1-\frac{20}{81}=\frac{61}{81}$.
Therefore, the answer is $D$.