There are four machines and it is known that exactly two of them are faulty. The

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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

Options:

A . 13

B . 16

C . 12

D . 14

Answer: Option B
:
B
This is a problem of without replacement.

P = \frac{o n e d e f . f r o m 2 d e f .}{a n y o n e f r o m 4} \times \frac{1 d e f . f r o m r e m a i n i n g 1 d e f .}{a n y o n e f r o m r e m a i n i n g 3}

Hence required probability =

\frac{2}{4} \times \frac{1}{3} = \frac{1}{6}

Aliter : Number of ways in which two faulty machines may be detected (depending upon the test done to identify the faulty machines) =

^{4} C_{2} = 6

Number of favourable cases = 1
[When faulty machines are identified in the first and the second test].
Hence required probability =

\frac{1}{6}

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