A man (M) and a woman (W) meet each other at an online dating website. They begin to date. After a year, M remembers that his account at the dating website is still active, and wants to delete it. So he logs in for a brief period, say 5 minutes. For the sake of this question, let us assume that the website does not allow him to permanently delete his account.
In a few minutes M receives a call from W!
W: What were you doing at that dating website?
M: I was trying to delete my account.
(Important: The only way W could have known that is that she must be logged in during that time also.)
M (continues): What were you doing there?
W: I had just logged in to see if your account was still active.
Question: M is suspicious that W just happened to be online at that very moment. He wants to have some mathematical measure of the following: Is it possible to calculate how often W must have been logged in every day or every week or whatever so that she happened to be online just at the same time?
(For example: The model may suggest she might be logged about half an hour everyday (or three times a week, or whatever) so that the incident occurred.
(I am aware that this may be a huge coincidence. I just want to know whether statistics has anything at all to say.)
Further question. (In my view, this should be workable somehow.) Exactly one year later the M logs in again to see whether he can now delete his account. Surprise, surprise! Another phone call from W! Leaving aside conspiracy theories (that W perhaps installed a spying software on M's computer, or whatever.)
Now M is really suspicious. Again: Is it possible to calculate how often W must have been logged in every day or every week or whatever so that she happened to be online just at the same time?
(Assume that at both times M was not aware that W was also online.)