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Probability: Mechanic and Defective Machines

XAT 2011 · Quantitative Ability & Data Interpretation · Medium · Probability

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There are four machines in a factory. At exactly 8 pm, when the mechanic is about to leave the factory, he is informed that two of the four machines are not working properly. The mechanic is in a hurry, and decides that he will identify the two faulty machines before going home, and repair them next morning. It takes him twenty minutes to walk to the bus stop. The last bus leaves at 8:32 pm. If it takes six minutes to identify whether a machine is defective or not, and if he decides to check the machines at random, what is the probability that the mechanic will be able to catch the last bus?

  1. A.

    0

  2. B.

    1/6

  3. C.

    1/4

  4. D.

    1/3

  5. E.

    1

Answer

D

Explanation

Time available to check = 32−20=1232 - 20 = 12 minutes, so he can test at most 2 machines. He will know the status of all 4 machines iff the two tested machines are either both defective or both non-defective. P(both defective)=16P(\text{both defective}) = \frac{1}{6}, P(both non-defective)=16P(\text{both non-defective}) = \frac{1}{6}. Total probability = 1/6+1/6=1/31/6 + 1/6 = 1/3.

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