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 5 match series India's second win occurs at the third test is:

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

Answer: (C)

Required probability = (Prob. of winning a test in the first two matches) . (prob. of winning a test in third match)
$= ^{2}C_{1} \left(\frac{1}{2}\right)^{2-1} \left(\frac{1}{2}\right)^{1}. \left(\frac{1}{2}\right) = \frac{2!}{1!} . \frac{1}{2}. \frac{1}{2}. \frac{1}{2} = \frac{1}{4} $