Discussion Forum : Probability I
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=one def. from 2 def.any one from 4×1 def. from remaining 1 def.any one from remaining 3
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

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