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The probability of India winning a test match against Australia is $\frac{1}{4}$ . Assuming the matches to be independent events, the probability that in a 7 match series Inida’s second with occurs at $4^{t h}$ test is P, then 256P is equal to

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answer is 27.

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Detailed Solution

2nd win in 4th test In the first 3 matches there must be exactly 1 win so, required probability

$=^{3} C_{1} {(\frac{1}{4})}^{1} {(\frac{3}{4})}^{2} (\frac{1}{4})$

$P = \frac{27}{256}$

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