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