A box contains 100 balls, numbered from 1 to 100 . If 3 balls are selected one after the other at random with replacement from the box, then the probability that the sum of the three numbers on the balls selected from the box is an odd number, is

Step-by-step solution

Probability(odd/even) = 1 2 For sum of three numbers on the balls to be odd: Case 1 - odd+odd+odd i.e. probability = 1 2 × 1 2 × 1 2 Case 2 - odd+even+even i.e. probability = 1 2 × 1 2 × 1 2 Case 3 - even+odd+even i.e. probability = 1 2 × 1 2 × 1 2 Case 1 - even+even+odd i.e. probability = 1 2 × 1 2 × 1 2 Hence, the required probability = 1 8 + 1 8 + 1 8 + 1 8 = 1 2