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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?
Sum
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Solution
Two tests will be required if the first machine is faulty and the 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 (1/2 + 1/2)`
= `2/3 xx 1`
= `2/3`
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