Unsolved Problem: Are Outcomes of Two Inspectors Independent?

[hypermonkey2]

Heres something i came across in a book but there's no solution...
take two inspectors in a factory (they can't talk to each other), and they inspect a series of products and they deem them defective or not. So the results would be (D,N), (N,N) ... where each coordinate is each inpectors verdict.
are the outcomes independent?

I would think not. But i cannot formalize that. thoughts?

 

[Pere Callahan]

How do the two inspectors determine whether a product shoud be deemed defective or not defective?

What exactly do you mean by independent outcomes? That the ratings for different products of the series are independent? Or that that the two inspectors' opinions on one fixed product are independent? Or something else?

To give an answer to any of these question you need to specify how the inspectors decide upon their opinion regarding a (maybe defective) item.

 

[hypermonkey2]

They inspect the product. Essentially, i think that IF we assume that they perform some sort of inspection, that IF one inspector deems it defective, that it is MORE likely that the product actually IS defective, so it is MORE probable that the second inspector deems it defective too.
In that sense, the outcomes are dependent, no?
Right, it is the products of the series that are independent.
What do you think?

 

[CRGreathouse]

Essentially, i think that IF we assume that they perform some sort of inspection, that IF one inspector deems it defective, that it is MORE likely that the product actually IS defective, so it is MORE probable that the second inspector deems it defective too.
In that sense, the outcomes are dependent, no?

I agree with you.

 

[hypermonkey2]

Great! How to formalize it?

 

[CRGreathouse]

You can't formalize the conclusion without the assumptions being formalized as well. Formalizing the assumptions would make the conclusion trivially follow.