## Question

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

### Solution

1/6

The probability that only two tests are needed = (probability that the first machine tested is faulty) × (probability that the second machine tested is faulty given that the first machine tested is faulty).

#### SIMILAR QUESTIONS

Let *A*, *B*, *C*, be three mutually independent events. Consider the two statements *S*_{1} and *S*_{2}.

*S*_{1} : *A* and *B* ∪ *C* are independent

*S*_{2} : *A* and *B* ∩ *C* are independent

Then

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