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.

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  1. What is the difference between independent and mutually exclusive events, if independent events are those which don’t change the probability of the other events?

  2. Hi had a doubt

    1) How independent evnnt is different than mutually exclusive event?

    2) How independent event is different than unconditiona ll event

  3. I don´t understand how knowing a die came up odd doesn´t change if our event one or two can take place. only one can take place now so shouldn´t the two events be dependant? cheers adn great vid

  4. Hi. In part “20:00” of video, you are saying A and B are dependent events based on weather etc. However, you said that given just two probabilities A and B we can never tell if its independent unless we know the intersection. How is A dependent on B and how can we show that? Thanks.

  5. Thank you for this post,

    Realizing independence(in the probability context) means equally proportional distribution is a great realization for me.