Question

The probability of India winning a test match against West Indies is $\frac{1}{2}$. Assuming independence from match to match, the probability that in a five match series India’s second win occurs at third test is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Given that
P(India wins) = $p=\frac{1}{2}$
$\therefore$ P(India loses) = $p^{\prime }=\frac{1}{2}$
Out of 5 matches, India’s second win occurs at third test. Hence, India wins third test and simultaneously it has won one match from first two and lost the other. Therefore, the required probability is
$P\left(LWW\right)+P\left(WLW\right)={\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{2}\right)}^3$
$=\frac{1}{4}$