Q. There are four machines and it is known that exactly two of them are faulty. They are tested, one by one in a random order till both the faulty machines are identified. Then, the probability that only two tests are needed, is
A) $\frac{1}{3}$
B) $\frac{1}{6}$
C) $\frac{1}{2}$
D) $\frac{1}{4}$
Explanation
(b)
The probability that only two tests are needed = (probability that the first tested machine is faulty) $\times$ (probability that the second tested machine is faulty given the first machine tested is faulty)$= \frac{2}{4} \times \frac{1}{3} = \frac{1}{6}$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.