If two events are independent this means the occurrence of one, doesn't affect the other, so as far as my understanding is concerned, this would mean that the intersection of their sample spaces is $\emptyset$, however , this isn't true. Why is this wrong?
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being tall and being good at math are independent. There are however tall people good at math. – Giulio R Nov 02 '22 at 14:13
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Building on the above (humorous) example, note that the assumption that the intersection is empty, is just false. – Gregory Nov 02 '22 at 14:14
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You have confused "mutually exclusive" with "independent." These are different concepts. – JMoravitz Nov 02 '22 at 14:14