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  4. 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 5 match series India's second win occurs at third test, is

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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 $5$ match series India's second win occurs at third test, is

IIT JEEIIT JEE 1995Probability

Solution:

Given, $P$ (India wins) $= 1/2 $
$\therefore \, P$ (India losses) $=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 $= P(LWW) + P(WLW)$
$ =\bigg(\frac{1}{2}\bigg)^3 +\bigg(\frac{1}{2}\bigg)^3=\frac{1}{4}$