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Follow the randomly-bouncing ball

Following the instructions gives us the following sequence: Now, we repeat, using the twelve letters we've extracted: Well, I don't know what that means. (Never mind the fact that I spaced it in a ...
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What's the correct intuition behind the expected number of die rolls until a 6 if all previous are even?

Okay, so you reset every odd roll. Therefore, E = E[6] + E[consecutive 2,4s before a 6]. E[6] is 1. E[2,4] = 1/3*E[2,4] -> E[2,4] = 1/2. So E=1+1/5 = 1.5. Expected Value is 1 1/2 dice rolls. Now, ...
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What's the correct intuition behind the expected number of die rolls until a 6 if all previous are even?

Well, you know that a roll can be either be a $2,4,6$, and it's the same chance for each, so it's $\frac{1}{3}$ for any of them. If you note that it's a geometric random variable, then it's ...
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