Rounding Probabilities...

The sample space is $S = (-0.50, -0.49, -0.8, ....,-0.01, 0.00, 0.01, ...., 0.49)$ Let E be the event that the round off error is at least 10 paise , then E' is the event that the round off error is at most 10 paise .

$E' = (-0.09, -0.08, ...., -0.01, 0.00, 0.01, ..., 0.09)$ $n(E') = 19 \quad and\quad n(S) = 100$ $p(E') = \frac {n(E')}{n(S)} = \frac {19}{100}$

$\Rightarrow Required\quad Probability,\quad p(E) = 1 - P(E')$ $= 1 - \frac{19}{100}$ $= \frac{81}{100} = \frac{a}{b}$ $\Rightarrow a + b = 81 + 100 = \boxed{181}$