The probability of India winning a test match against West Indies is `1/2.` Assuming independence from match to match, find the probability that in a match series India’s second win occurs at the third test.

Explanation

To solve the problem, we need to find the probability that India's second win occurs at the third test match. Given that the probability of India winning a match (W) is \( P(W) = \frac{1}{2} \) and the probability of losing a match (L) is \( P(L) = 1 - P(W) = \frac{1}{2} \).

### Step-by-Step Solution:

1. **Identify the Events**:
- We want the second win (W) to occur on the third test. This means we need to consider the outcomes of the first two tests.
- The possible sequences for the first two tests that allow the second win to occur on the third test are:
- Case 1: Win (W), Lose (L), Win (W) → W, L, W
...