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Jabbed/dead on the same day?

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A popular habit amongst certain ... people is to amplify reports where someone had a vaccine and died within a short period after. Of course, they take no care to check what the background rate might be given no correlation. Essentially, this is an 'overlap' problem: the likelihood of intersect between two sets m (today's vaccinees) and n (today's deaths) drawn independently from a population N. Since you only die once, or get vaccinated once on any given day, it is sampling without replacement.  Let's take the US.  N is 330 million.  m (set 1) is the number of vaccinations in a day, say 1 million.  n (set 2) is the number of cardiovascular deaths a day, which is about 2380.  So what's the probability that at least 1 person in the 'vaccinated today' set will also be in the 'death today' set? The calculation itself is fiddly***, but I like this  calculator . The example is picking marbles, but it is much the same thing. There are 330 million '