easy Probability
A release-checked easy problem for training Expected Value/LOTUS, Dice.
A standard fair n-sided die is rolled infinitely. The cumulative sum of all observed rolls is recorded after each roll. For each integer $k \geq 1$, let $f(n,k)$ be the probability that the cumulative sum is ever exactly $k$. For a fixed $k$, compute $\displaystyle \lim_{n \rightarrow \infty} f(n,k)$. Report the answer when $k = 6$.
This Probability problem is tagged Expected Value/LOTUS, Dice. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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