Calculating the change in the chance of something happening

[vkthawaii]

To start I want to say that this is not a school question, and I am not in a statistics class, nor do I know if my question is even answerable.
But anyway, here's my question: Statistically, snow in October in Washington D.C. should occur once every 43.3 years. But, in any given year, the chance is only 2.3%. How does the percent chance change as you get closer to a multiple of 43.3? Does it change at all?
I was thinking maybe something like: DeltaP = 43.3x - T
In which the change in percent chance (DeltaP) is equal to the difference between the current time (T) and any multiple of 43.3 (43.3x).
Ideally you would be able to somehow get a function that could be graphed, or be able to solve for the percent chance at any given time.
Any suggestions?

 

[Dr.Peterson]

I suspect you are falling victim to the Gambler's Fallacy, in which you think that the probability of an event is affected by past events (like thinking you are more likely to roll a certain number on a die if it hasn't come up recently).

If there is a certain probability of snow in any given year (and there is nothing changing in the environment that would modify that probability), that doesn't change as snowless years accumulate.

To put it another way, when we say an event on average happens every 43.3 years, that does not mean it happens cyclically, and is more likely to happen 43.3 years after the last time it happened, than any other time. It only means that, say, if you record when it happens over 1000 years, it can be expected to happen about 1000/43.3 = 23 times (that is, 2.3% of the time, as you indicated). Probability is a long-term average, not a short-term expectation.

Similarly, a die will roll a 1 on average every 6 rolls, in the sense that 1/6 of all rolls, in the long run, can be expected to be 1. This does not mean that every 6th roll is more likely to be a 1.

So there is an answer to your question. Delta P is 0.