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

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

This is a problem of without replacement.
$P=\frac{\text{one def. from 2 def.}}{\text{any one from 4}}\times \frac{\text{1 def. from remaining 1 def.}}{\text{any one from remaining 3}}$
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 = $\frac{1}{6}$