1. P(B)P(A|B) = P(A)P(B|A)

    But if A and B are not independent, then what is the P(A) or P(B)? Are they really just P(A|(B or ¬B)) and P(B|(A or ¬A))?

    And what if A and B are dependent on themselves and on C?
    Multi-?variable? Bayes? Theorem?

  2. the brother example is wrong. You made the video in a hurry probably. The two brothers dead at the same time is actually 1/4X1/4. The P(A)xP(A|B) implies a sequence of events and not simultaneity (you AND your brother). I really like your videos but please put a little more time in them because fallacy is in all of us. I can see that this one is made in a hurry.

  3. Just a slight suggestion in notation: writing P(A | B)P(B) instead of P(B)P(A | B)
    This may help in marginalization e.g. P(A) = ∫ P(A | B) P(B) dB
    I personally liked this order more because it seems to "cancel out" the given part B in the likelihood P(A | B) with the prior P(B).

    Anyway, I liked your video so much!

  4. @3Blue1Brown have you ever considered becoming a content writer for Brilliant? Not that I work for them or anything, but your graphical explanation skills would seriously up their game…

  5. 3Blue1Brown I really like your videos, they are really helpful, but I noticed a small tweak that you could make, the 3Blue1Brown circle from the intro from some of your older videos is more detailed than the one in more recent videos and for your actual channel, so could you please bring back the more detailed one and change the one for your channel to make it more detailed? Thank you.

  6. I have a problem and i need serious help : u know that when u have a vector field , a function and a curve u can calculate the line integral which result is the work . I want to invert it , i have the vector field and i want to find a curve on which the work is maximum , i dont even know where to start searching , any references please tell me .

  7. Amazing. Used this all the way through university and never really understood what the implications where of independency. You sir have shown me how relevant it is.

  8. I personally think it’s better phrased as P(A|B)/P(B|A)=P(A)/P(B) because then, it doesn’t matter what data we’re missing, it’s easy to solve because we’ve grown familiar to such equations

  9. One thing about independence though is that it's not just a special case of a mathematical formula, it caries implications about the physical relationship between things being modeled. The link between the metaphysical concept of independence and the mathematical formula is the foundation for many theories of epistemology.

  10. Hello, I love your videos; and see you are a very gifted mathmetician! Could you please do a video (or a few) about sacred geometry. I think it can get alot of people interested in mathematics, and it's beauty. I cried reading a book. Cheers 😃! You're the best!

  11. You’re probably not gonna read this, but I recently went to a university and checked out the math department. And there was this guy who was explain to me what things they cover in the study, and I was flexing my brain muscles on how much I knew. Later he asked me, do you watch 3Blue1Brown? So I of course said yeah. He just said, yeah that explains it.

  12. Grant, if you created a course on Udacity or Udemy on scientific and mathematical graphical programming; it'd make you, even more of, a millionaire. As well as teaching thousands of people the incredible art of better visual communication of advanced concepts. The impact of which, on global education, is hard to even imagine.

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