A box contains 100 balls, numbered from 1 to 100 . If 3 balls are selected one after the other at random…

Probability(odd/even)$=\frac{1}{2}$

For sum of three numbers on the balls to be odd:

Case 1 - odd+odd+odd

i.e. probability$=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}$

Case 2 - odd+even+even

i.e. probability$=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}$

Case 3 - even+odd+even

i.e. probability$=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}$

Case 1 - even+even+odd

i.e. probability$=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}$

Hence, the required probability$=\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}=\frac{1}{2}$