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.

[alannnnnnz]

You're one youtube channel that actually explains stuff cleary and in an understandable way. Thank you so much sir!

[Marco-wzxw]

Simply incredible lesson. Exactly what I was looking for, with rigorous and practical explanations. Thank you.

[ovodot]

Glad to see you back. I have watched your videos on inference and hypothesis testing over and over again. I have used your videos to educate non-english speaking students in Greece. Hope you carry on with the good work. You and Khan Academy and 3blue1brown are amazing!!!! Your contribution to education and therefore to science is huge!

[dddd-cizm]

An recent study showed a coin toss depends on it original starting side. So the last part of the video about "not being able to prove it "mathematically" is spot on

[tonyjames]

Thank you for this post,

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

[jathebest]

Sir, don't forget our society is growing better because educational YouTubers like you exist. I even learn programming by engaging online and I need to learn statistics a bit for my Python programming. Huge thanks from South Korea!

[rsaleh]

So easy to understand. The voiceover is silky smooth too. Great combination for learning.

[kedarlele]

The content here is exceptional ! Great job Sir !

[henrychan]

The last example wakes me up and reminds me to think out of the box. Thanks!

[koungmeng]

Thanks. This video helps me greatly. The meaning of Independent in probability is different from normal day-to-day English.

[ASLUHLUHC]

Nice stuff. Found your channel through some random comment on a 3Blue1Brown video

[mochhisyamtanzil]

you saved me on my econometrics, thank you so much

[hambonefakenamington]

thank you, this really helped me get a thorough gist of independence!

[hillarydunkens]

I’m currently in 7th grade and I have a quiz on this. Thank you for making this video it really helped

[linans]

this is really helpful explained simply and in a really easy way to understand. thank you so much for this.

[thedeathofbirth]

Jb, you are very clear in your teaching, makes it easy to grasp the subtle points that cause most beginners to come to the wrong answer. Can you please make videos when the unconditional probabilities are not given but depend on each other? For example, what is the probability of a 3rd girl if there are two girls in a family already OR what is the probability of the second child being a girl if the oldest is a girl? I have difficulty when the sample space becomes the second even, do I make sense? Thank you so very much for making this world more tolerable. Some post pitiful hate contents or violent videos and some are like you...

[normanremedios]

Thank you so much for your response. A subject ignored in texts but important nevertheless less.As usual you have not disappointed..

[richardjohnson]

it's crystal clear now what INDEPENDENCE means Thank you

[JonathanHernandez-mjhr]

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

[Angela-oyqs]

You just saved my stats grade. thank you!