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EMP Q.34

0. Three machines M1, M2 and M3 produce identical
items. Of their respective output 5%, 4% and 3%
of items are faulty. On a certain day, M1 has
produced 25% of the total output, M2 has produced
30% and M3 the remainder. An item selected at
random is found to be faulty. What are the chances
that it was produced by the machine with the
highest output?

  • Option : C
  • Explanation : Let the event of drawing a faulty item from any of the machines be A, and the event that an item drawn at random was produced by Mi be Bi' To P (Bi/A) proceed as follows:

    Probability

    The highest output being from M3 required probability

    =  Probability

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