# There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then the proability that only two tests are need is

25 Points
13 years ago

Only 2 tests will be needed to find the faulty machines if we can find one faulty machine in each test

Probality that we will test a faulty machine in first test is 2/4=1/2 (there are 4 machines and 2 of them faulty)

Now that one faulty machine has been identified we are left with 3 machines with one of them being faulty.Probaility that we will test the other faulty machine in second test is 1/3.so probability that we will require 2 tests to find the faulty machines is 1/2*1/3=1/6

ALL THE BEst

ABhinav Batra

Avijit Arya
33 Points
13 years ago

Hi,

there are 2 ways of getting the machines in the first 2 tries. First possibility, you get both faulty, or you get both correct(since, then you know the left ones are faulty). Thus solving both possibilities: (2/4)x (1/3) x 2 since both have same chances. Hence solving Answer is: 1/3

Thanks