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Bob throws the ball into bucket with paint. One half of the ball is painted now (lower hemisphere). Then he picks it up and rotates randomly. Then he throws ball again into bucket with paint. And repeats this process until all ball gets painted.

Question: What is the average number of throws to get all the ball painted?

I don't understand how to use continuous probability here. Or maybe Law of Large numbers?

Grigori
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    Related: https://math.stackexchange.com/questions/4229360/expected-value-of-interesting-random-variable-on-sphere and https://mathoverflow.net/questions/33112/estimate-probability-0-is-in-the-convex-hull-of-n-random-points – Henry Aug 23 '21 at 07:59
  • @Henry, Thank you! First link is exactly what I needed. – Grigori Aug 23 '21 at 08:17

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