Q. The probability of India winning a test match against West-Indies is $\frac{1}{2}$ 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) $\frac{2}{3}$
Explanation
(b)
Required probability
$P\left( A_{1} \cap A_{2}^{'} \cap A_{3} \right) + P(A_{1}' \cap A_{2} \cap A_{3})$
$= P\left( A_{1} \right)P\left( A_{2}^{'} \right)P\left( A_{3} \right) + P\left( A_{1}^{'} \right)P\left( A_{2} \right)P(A_{3})$
$= \left( \frac{1}{2} \right)^{3} + \left( \frac{1}{2} \right)^{3}$
$= \frac{1}{8} + \frac{1}{8} = \frac{1}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.