Question

The probability of India winning a test match against South Africa is $1 / 2$ assuming independence form match to match played. The probability that in a match series India's second win occurs at the third day is

• A. $\frac{1}{8}$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $\frac{2}{3}$

Answer 1

Answer: (C)

Given, probability of winning a test match, $P(W)=\frac{1}{2}$
Probability of lossing a match, $P(L)=1-\frac{1}{2}=\frac{1}{2}$
Probability that India's second win occurs at the third day
$=P(L) \cdot P(W) \cdot P(W)+P(W) \cdot P(L) \cdot P(W)$
$ =\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2}+\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2}=\frac{1}{8}+\frac{1}{8}=\frac{1}{4}$