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The exercise says like this:

Two inspectors $A$ and $B$ independently inspected the same batch of articles. 4% of items are defective. The examination showed that:

  • 5% of items are considered defective by $A$.
  • 6% of items are considered defective by $B$.
  • 2% of items are correctly considered defective by $A$.
  • 3% of items are correctly considered defective by $B$.
  • 4% are considered defective by both $A$ and $B$.
  • 1% are considered correctly defective by both $A$ and $B$.

$a)$ Construct a Venn diagram, which shows the percentages of the items in the 8 possible disjoint classes, motivated by the classification of the inspectors and the actual classification of the articles.

$b)$ What percentage of the articles are defective but are considered as if not by both inspectors?

And I have something like this:

enter image description here($C$ is "correctly defective")

So, the answer means $C∩(A∪B)^c$, the blue zone?

  • 1
    There's something wrong with your Venn diagram. B only considers 6% of items defective, but you've got a total of 9 in that circle. – 2017-01-23
  • 0
    Thanks. Now I have fixed it. Your answer is equal to $C∩(A∪B)^c$, the blue zone? – 2017-01-23
  • 0
    Yes, that's correct. – 2017-01-23

1 Answers 1

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4% of items are actually defective. 1% are considered so by both A and B; that leaves 3% that are correctly considered defective by at most one inspector. A correctly considers a total of 2% defective; that means 1% beyond the overlap. B correctly considers a total of 3% defective; that means 2% beyond the overlap. That adds up to 3% beyond the overlap that are correctly considered defective by at least one inspector. There was only 3% left over; that means that there's nothing left to be defective but not considered defective by either inspector. So, 0%.