Q45 / 120 · VITEEE 2016 · Mathematics
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$\frac{1}{8}$
- Correct answerB$\frac{1}{4}$
- C$\frac{1}{2}$
- D$\frac{2}{3}$
Solution
Required probability
$$
\begin{array}{l}
=\mathrm{P}(\text { First win }) \times \mathrm{P}(\text { First win }) \times \mathrm{P}(\text { Second } \\
\text { win) } \\
+\mathrm{P}(\text { First Defeat }) \times \mathrm{P}(\text { First win }) \times \mathrm{P}(\text { Second } \\
\text { win) } \\
=\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}+\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}=\frac{1}{4}
\end{array}
$$
Hence, the correct answer is option: 'B'.