I'm having difficulty explaining why disjoint events are not independent. YMM states, "If A and B are disjoint, then the fact that A occurs means B cannot occur. So disjoint events are not independent." I'm ok with the first part but I'm having difficulty coming up with an example to show that disjoint events are not independent.
Al Reif wrote <Disjoint events cannot occur simultaneously. When rolling a die, you <could roll a 3 [Event A] or roll a 4 [Event B]. But you cannot roll a 3 and a 4 at the same time with one die. In contrast, rolling a 3 <[EventA] and having blonde hair [Event B] are not disjoint--they can happen at the same time.
But isn't rolling a 3 or a 4 on a die independent?
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