There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, is a random order till both the faulty machines are identified. Then the probability that only two tests are needed
A
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B
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C
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D
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Solution
The correct option is B This is a problem of without replacement. P=onedef.from2def.anyonefrom4×1def.fromremaining1def.anyonefromremaining3 Hence required probability = 24×13=16 Aliter : Number of ways in which two faulty machines may be detected (depending upon the test done to identify the faulty machines) = 4C2=6 Number of favourable cases = 1 [When faulty machines are identified in the first and the second test]. Hence required probability = 16