The probability of India winning a test match | vedclass

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(C) Let $W$ denote a win and $L$ denote a loss for India. The probability of winning $P(W) = \frac{1}{2}$ and the probability of losing $P(L) = 1 - \f

Vedclass · Accepted Answer

$\frac{1}{4}$

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(C) Let $W$ denote a win and $L$ denote a loss for India. The probability of winning $P(W) = \frac{1}{2}$ and the probability of losing $P(L) = 1 - \frac{1}{2} = \frac{1}{2}$.For the second win to occur exactly at the third test match,India must have won exactly one match in the first two tests and then won 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 $P(L) 	imes P(W) 	imes P(W) = \frac{1}{2} 	imes \frac{1}{2} 	imes \frac{1}{2} = \frac{1}{8}$.The probability of the sequence $(W, L, W)$ is $P(W) 	imes P(L) 	imes P(W) = \frac{1}{2} 	imes \frac{1}{2} 	imes \frac{1}{2} = \frac{1}{8}$.The total probability is the sum of these two mutually exclusive events: $\frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}$.

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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