For two random cuts, I have 1/3 chance to have 4 and 2/3 chance to have 3. So expectation is 10/3. What about 3 cuts or even n cuts? Are there any general results?
2026-03-29 15:15:20.1774797320
Make three random cuts to a circle, what is the expected number of areas produced?
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In the crude diagram below, we can see $4$, $5$, $6$, and $7$ areas resulting from $3$ cuts. There is no easy way to tell which is more likely.