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

Question

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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