IIT-JEE 1998Question 1
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
Probability
Solution
Two tests suffice iff the first two machines tested are both faulty or both good: $\frac{2}{4}\cdot\frac13+\frac24\cdot\frac13=\frac13$.