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

Answer 1

Answer: (B)

$\frac{1}{4}$

Required probability
$=P\left(Firstwin\right)\times P\left(Firstdefeat\right)\times P\left(Secondwin\right)+P\left(Firstdefeat\right)\times P\left(Firstwin\right)\times P\left(Secondwin\right)$

$=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}+\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{4}$