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Three machines M1, M2 and M3 produce nominally identical items. The evidence of the engineers past...

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Statistics

Three machines M1, M2 and M3 produce nominally identical items.The evidence of the engineers past experience is that 5 % of theoutput from machine M1 is faulty, 3.5 % of the output from machineM2 is faulty and 2.5 % of the output from machine M3 is faulty. Ona given day, M1 has produced 15 % of the total output, M2 hasproduced 30 % and M3 the remainder.

An item selected at random is found to be faulty.

  1. Use Bayes' theorem to find the probability that it was producedby M1.
  2. Use Bayes' theorem to find the probability that it was producedby M2.
  3. Use Bayes' theorem to find the probability that it was producedby M3.

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