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I am working through some practice questions in a statistics textbook and I am struggling to understand why I got this question wrong. This is the context for the question:

The AAPOR is an association of about 1600 individuals who share an interest in public opinion and survey research. They report that typically as few as 10% of random phone calls result in a completed interview. Reasons are varied, but some of the most common include no answer, refusal to cooperate, and failure to complete the call. Which of the following events are independent, which are disjoint, and which are neither independent nor disjoint?

This is the set of events that I gave the wrong answer for:

A: your telephone number is randomly selected. B: you're not at home at dinnertime when they call.

I answered as "neither independent nor disjoint" and the answer was "independent".

The way I approached this was that if event A doesn't happen, then the interviewers will never call, i.e. P(B|not A) = 0. However, P(B|A) > 0.

Provided I haven't made a mistake there, it seemed to me that knowing whether event A happens or not changes the likelihood of event B. On reflection, of course there are two parts to event B (you are not at home; they call) so I might be getting stuck because A has to be the precursor to B, but if that's the case I'm still not sure how it would follow that they are independent events.

Thank you for your help.

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I feel your question concerns more the interpretation than anything else, because there seems to be a hidden assumption that

Your telephone number is randomly selected -> they call

Under this assumption I would rephrase the question as

A: they call. B: you're not at home at dinnertime when they call.

Now your being home at dinnertime is independent of the event they call, well, unless you have a super power to predict their random picking of your number and you don't really love their calls :-)

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    $\begingroup$ I see! Thank you! $\endgroup$ – blue Apr 8 at 23:29

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