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
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- $\dfrac{1}{2}$
- $\dfrac{3}{4}$
- $\dfrac{3}{8}$
- $\dfrac{1}{8}$
The Correct Option is C
Solution and Explanation
We want the sum of three numbers to be odd. That happens when either: - (Odd, Odd, Even) → 3 combinations - (Odd, Even, Odd) → 3 combinations - (Even, Odd, Odd) → 3 combinations
Total 3 combinations where 2 are odd and 1 even.
Each event has probability: $\left(\frac{1}{2}\right)^3 = \frac{1}{8}$
Total probability = $3 \times \frac{1}{8} = \frac{3}{8}$
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