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.