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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 probability that only two tests are needed is
  • a)
    1/3
  • b)
    1/6
  • c)
    1/2
  • d)
    1/4
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
There are four machines and it is known that exactly two of them are f...
Solution:

Understanding the problem:
- There are four machines, with exactly two of them being faulty.
- The machines are tested one by one in a random order until both faulty machines are identified.

Calculating the probability:
- The total number of ways to choose 2 faulty machines out of 4 is C(4, 2) = 6.
- The probability that the first two machines tested are both faulty is 2/4 * 1/3 = 1/6.
- The probability that the first machine is faulty and the second one is not faulty is 2/4 * 2/3 * 1/2 = 1/6.
- The total probability that only two tests are needed is the sum of the above two probabilities, which is 1/6 + 1/6 = 1/3.
Therefore, the correct answer is option B) 1/6.
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Community Answer
There are four machines and it is known that exactly two of them are f...
The probabiity that only two tests are neded
= Probability that the first machine tested is faulty) x (probability that the second machine tested is faulty given that the first machine tested is faulty).
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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 probability that only two tests are needed isa)1/3b)1/6c)1/2d)1/4Correct answer is option 'B'. Can you explain this answer?
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