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Question
There are three machines and 2 of them are faulty. They are tested one by one in a random order till both the faulty machines are identified. What is the probability that only two tests are needed to identify the faulty machines?
Solution
Two tests will be required if first machine is faulty and second is good OR both machines are faulty.
Probability that only two tests are needed
= `2/3 xx 1/2 + 2/3 xx 1/2`
= `2/3`
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