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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, in a random order till both the faulty machines are identified. Then the proability that only two tests are need is

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

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2 Answers

AskiitiansExpert Abhinav Batra
25 Points
11 years ago

Dear Padmavithi

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
10 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

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