The probability of India winning a test match against West Indies is given as 1/2. Assuming independence from match to match, we need to find the probability that India's second win occurs in the third test of a 5-match series.

Let's break down the problem into smaller steps:

Step 1: Probability of India winning a single match
The probability of India winning a single test match against West Indies is given as 1/2. This means that in any given match, there is a 1/2 chance that India will win.

Step 2: Probability of India losing a single match
Since the probability of India winning a match is 1/2, the probability of India losing a match is also 1/2. This means that in any given match, there is a 1/2 chance that India will lose.

Step 3: Probability of India winning a specific match in the series
In a 5-match series, we want to find the probability that India's second win occurs in the third test. This means that India must win the first two matches and then win the third match.

The probability of India winning the first match is 1/2.
The probability of India winning the second match is also 1/2.
The probability of India winning the third match is also 1/2.

Since the matches are assumed to be independent, we can multiply the probabilities to find the probability of all three events happening:

(1/2) * (1/2) * (1/2) = 1/8

Step 4: Probability of India losing the remaining matches
After India wins the first three matches, there are two matches remaining. Since we are looking for the probability of India's second win occurring in the third test, India must lose the fourth match. The probability of India losing the fourth match is 1/2.

Step 5: Probability of India winning the fifth match
In order for India's second win to occur in the third test, India must also win the fifth match. The probability of India winning the fifth match is 1/2.

Step 6: Multiply the probabilities
To find the probability of India's second win occurring in the third test, we multiply the probabilities of the individual events happening:

(1/8) * (1/2) * (1/2) = 1/32 ≈ 0.03125

Therefore, the probability that India's second win occurs in the third test of a 5-match series is approximately 0.03125, which rounded to two decimal places is 0.03 or 0.03.