SOLUTION: A quality controller of a manufacturing company has sampled 25 items from the production line. An item will pass the test if it has no defect, but if it is defective, further tes

Algebra ->  Probability-and-statistics -> SOLUTION: A quality controller of a manufacturing company has sampled 25 items from the production line. An item will pass the test if it has no defect, but if it is defective, further tes      Log On


   

Question 1152612: A quality controller of a manufacturing company has sampled 25
items from the production line. An item will pass the test if it has
no defect, but if it is defective, further test will determine whether
it is minor or major defect. Of the 25 sampled items, 4 have minor
defects and 2 have major defects. What is the probability that an
item has major defect, given that it is defective?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Obviously, you should relate 2 with major defects to to the total of 6 = 4+2 defective.


The answer is  P = 2%2F6 = 1%2F3.

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Notice that the problem's formulation is  ambiguous.

Because it does not instruct the reader if these  4  minor and  2  major defects are for separate items,  or  2  are the part of  4.

I solved the problem assuming that they are separate,
but another interpretation is  ALSO  POSSIBLE,  leading to another answer.


Actually,  it is a  BIG  FAULT  when the problem admits different interpretations.