The probability of India winning a test match | vedclass

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(C) Let $p$ be the probability of winning a match,$p = \frac{1}{2}$.Let $q$ be the probability of losing a match,$q = 1 - p = \frac{1}{2}$.For India's

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$\frac{1}{4}$

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(C) Let $p$ be the probability of winning a match,$p = \frac{1}{2}$.Let $q$ be the probability of losing a match,$q = 1 - p = \frac{1}{2}$.For India's second win to occur at the third test,India must win exactly one match in the first two tests and win the third test.The possible sequences for the first three matches are $(L, W, W)$ and $(W, L, W)$.The probability of the sequence $(L, W, W)$ is $q 	imes p 	imes p = \frac{1}{2} 	imes \frac{1}{2} 	imes \frac{1}{2} = \frac{1}{8}$.The probability of the sequence $(W, L, W)$ is $p 	imes q 	imes p = \frac{1}{2} 	imes \frac{1}{2} 	imes \frac{1}{2} = \frac{1}{8}$.The total probability is $\frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}$.

$x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(x)$	$0$	$2k$	$k$	$3k$	$2k^2$	$2k$	$k^2+k$	$7k^2$

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

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