The probability of India winning a test match against west Indies is ½. Assuming independence from match to match the probability that in a 5 match series India’s second win occurs at third test is

 :    P ( India wins) = p = 1/2
$\Rightarrow$ P ( India loses) = q = 1/2
Out of 5 matches India’s second win occurs at third test
$\Rightarrow$ India wins third test and simultaneously it has won one match from first two and lost the other.
$\therefore$ Required probability = P (LWW) + P (WLW)

$={\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{2}\right)}^3=\frac{1}{4}$