Question

The probability of India winning a test match against Australia is $\frac{1}{2}$ assuming independence from match to match. The probability that in a match series India�s second win occurs at third test match is

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

Answer 1

Answer: (B)

$\frac{1}{4}$

Answer 2

Required probability = P (First win) $\times$ P(First win) $\times$ P(Second win) + P(First Defeat) $\times$ P(First win) $\times$ P(Second win) $= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} + \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2} = \frac{1}{4}$