Question

A sum of money rounded off to the nearest rupee. The probability that the error occured in rounding off at lest 10 paise is

• A. $\frac{29}{100}$
• B. $\frac{30}{100}$
• C. $\frac{70}{100}$
• D. $\frac{81}{100}$

Answer 1

The correct option is D $\frac{81}{100}$

Here, Sample space $S=-0.50,-0.49,-0.48,...,-0.01,0.00,\mathrm{0.01...0.44}$
Let $A$ be the event that the rounded off error is at least $10$ paise.
Then $A$ is the event that the rounded off error is at most a paise.
Sample space for $A$ is given by $-0.09,-0.08,...,-0.01,0.00,\mathrm{0.01...0.09}$
$\therefore P\left(A^S\right)=\frac{19}{100}\Rightarrow 1-P\left(A\right)=\frac{19}{100}\Rightarrow P\left(A\right)=\frac{81}{100}$