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//2`
C. `1//4`
D. `2//3`

Answer

C

Explanation

Given, probability of winning a test match, `P(W)=(1)/(2)`
Probability of lossing a match, `P(L)=1-(1)/(2)=(1)/(2)`
Probability that India's second win occurs at the third day
`=P(L).P(W).P(W)+P(W).P(L).P(W)`
`=(1)/(2).(1)/(2).(1)/(2)+(1)/(2).(1)/(2).(1)/(2)=(1)/(8)+(1)/(8)=(1)/(4)`