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Q.

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

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a

$\frac{1}{8}$

b

$\frac{1}{4}$

c

$\frac{1}{2}$

d

$\frac{2}{3}$

answer is B.

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Detailed Solution

P ( India winning a test match against west-in dies) $= \frac{1}{2}$

$P (Loss) = 1 - \frac{1}{2} = \frac{1}{2} \begin{matrix} 1 & 2 & 3 \\ W & L & W \\ L & W & W \end{matrix} \begin{matrix} Probability \\ \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \\ \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \end{matrix}$

$∴$ Probability $= 2 \times \frac{1}{8} = \frac{1}{4}$

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