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

$\frac{1}{6}$

The total number of ways in which two machines can be chosen out of four machines is ${^4C}_2 = 6$.

If only two tests are required to identify faulty machines, then in first two tests faulty machines are identified. This can be done in one way only.

So, favourable number of ways = 1.

Hence, required probability = $\frac{1}{6}$.