First slide

Theorems of probability

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

Moderate

A

$\frac{1}{8}$
B

$\frac{1}{4}$
C

$\frac{1}{2}$
D

$\frac{2}{3}$

Solution

Given that
$P (India wins) = p = 1 / 2$
$∴ P (India loses) = p^{'} = 1 / 2$
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
$\begin{matrix} P (LWW) + P (WLW) = {(\frac{1}{2})}^{3} + {(\frac{1}{2})}^{3} \\ = \frac{1}{4} \end{matrix}$

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