The probability of India winning a test match against West Indies is 1/2. Assuming independence from match to match, find the probability that in a match series Indias second win occurs at the third test.

Options

A. `1/8`
B. `1/4`
C. `1/2`
D. `2/3`

Answer

B

Explanation

Given P(India wins ) =1/2
`:.` P (India losses) =1/2
Out of 5 matches India 's second win occurs at third test .
`implies` India wins third test and simultaneously it has won one match from first two and lost the other .
`:.` Required probability =P(LWW)+P(WLW)
`=((1)/(2))^(3)+((1)/(2))^(3)=(1)/(4)`