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Independent Events (Basics of Probability: Independence of Two Events)

An introduction to the concept of independent events, pitched at a level appropriate for the probability section of a typical introductory statistics course. I give the definition of independence, work through some simple examples, and attempt to illustrate the meaning of independence in various ways. (Note: I use the phrase "not independent" rather than "dependent" almost exclusively. There is nothing wrong with calling events dependent when they are not independent, but I prefer to use "not independent" for a couple of reasons.) (I'm on a bit of a probability run, but looking forward to getting back to statistics videos in the near future.) This one turned out to be long, as I had a number of points I wanted to discuss. Here's the breakdown: 0:20. The definition of independence, showing what that means in terms of conditional probability, and some hand-waving discussion of what independence means. 3:48. Very simple examples (P(A) = x, P(B) = y, etc.). 6:20. Die rolling examples. 10:03. Discussion of the fact that if A and B are independent, so are (A and Bc), (Ac and B), and (Ac and Bc), including a hand-waving justification. The previous example involved a lead-in to this. (The hand-waving is legit happening behind the scenes.) 11:15. Visual illustration of independence. 14:39. Playing card examples. 18:19. Discussion of how we sometimes assume events are independent (e.g. heads on first toss of a fair coin, heads on second toss), and how this is an *assumption*, and not something that can be proven mathematically (despite what you might see elsewhere). 19:24. Discussion of how the term "independent" can have a different meaning in everyday English compared to its usage in probability, and how that is sometimes a cause for confusion.