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← 5 Flips 3 Heads Solution - Intro to Statistics

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Showing Revision 4 created 05/25/2016 by Udacity Robot.

  1. And the log is 10 again. There's two proofs.
  2. One is I can just flip heads into heads. So three heads means two tails.
  3. I can give the exact same game as before where I placed tails as opposed to heads
  4. and it gives me the same equation as before, but let's do it the new way, three heads.
  5. I can place 543--the first heads, the second and the third.**
  6. For the first, I have five positions, for the second--four, and for the third--three are left.
  7. This gives me the common networks for those heads, but now I'm over counting.
  8. How much am I over counting?
  9. Well, suppose I'm committed to put the three heads into the three slots over here and that's not given.
  10. And I just wonder in which order I've put them in,
  11. so I might put the first one here, the first one here, the first one here.
  12. Then for the first one placed in here, there's now three different ways of placing it.
  13. For the second one, there's two different ways of placing it.
  14. For the third one, it's not deterministic--there's just one slot left.
  15. So I over count this by a factor of 6--there are 6 different ways of placing these three heads
  16. into these three slots, so the result is 543/321 producing the 5*2=10.*
  17. And that is insightful.