Question

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 third test is

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

Answer 1

The correct option is B $\frac{1}{4}$

India's second win in the third match can happen in the following ways:
Win in the first match, loss in the second and win in the third OR
Loss in the first match, win in the second and win in the third.
Probability of winning = $\frac{1}{2}$ and the probability of losing = $1-\frac{1}{2}=\frac{1}{2}$.
Therefore, the required probability = $\frac{1}{2}\ast \frac{1}{2}\ast \frac{1}{2}+\frac{1}{2}\ast \frac{1}{2}\ast \frac{1}{2}=\frac{1}{8}+\frac{1}{8}=\frac{1}{4}$