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"Happens every X updates" vs. "Has Y% of happening every update" - Main differences?

Example: I call my parents once a week, every Saturday. There is a 14% chance (1/7) that my parents will call me once at any day of the week.

I'm having a hard time to figure out the main differences of those scenarios. After a long time, the total amount that both happened will be approximate. However, the first will never go above or below the predicted.

What are the main differences? How it behaves according to the frequency of the updates?

Hope it is clear enough. This is not only for theoretical purposes, I just used the example above for the abstraction of each case.

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    The first *always* occurs; the same thing happens each and every week. The second one is a probability; it may not occur for a long run, it may occur a lot of times in a row. It's true that "in the long run" you expect your parents to call you the same number of times you call them, but whereas you *always* call them exactly once on any given 7 day period, the same cannot be said of your parents calling you.2012-04-20

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Taking you example with calling parents, let $A_{d}$ denote the event of you calling your parents on the day $d$ and $B_{d}$ the even of your parents calling you. Then, the first phrase says that \begin{align*} &P(A_{Saturday}) = 1, \\\ \forall d\neq Saturday.\ &P(A_{d}) = 0, \\\ \end{align*} where the second phrase says that $\forall d.\ P(B_{d}) = 1/7 .$

The average calling rate is the same, however your parents can predict with 100% accuracy which day you will be calling, and your prediction of their calls will be much worse. What distinguishes those cases even more: there will be exactly one your call every week, however, in a given week, there could be even 7 calls from your parents, also there may not call at all (the whole range is possible).