Question

The probability of India winning a test match against West-Indies is 1 / 2 assuming independence from match to match. The probability that in a match series India's second win occurs at the third test is :

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

Answer 1

Answer: (B)

Required probability
$=P\left(A_{1} A_{2}^{\prime} A_{3}\right)+P\left(A_{1}^{\prime} A_{2} A_{3}\right)$
$=P\left(A_{1}\right) P\left(A_{2}'\right)$ $P\left(A_{3}\right)+P\left(A_{1}^{\prime}\right) P\left(A_{2}\right) P\left(A_{3}\right) $
$=\left(\frac{1}{2}\right)^{3}+\left(\frac{1}{2}\right)^{3}=\frac{1}{8}+\frac{1}{8}=\frac{1}{4}$