How would you explain or visually show someone the difference between linear/static probability vs dynamic?

Question

Forgive me if I'm using the wrong terminology, but I'm attempting to explain to a non-technical person the difference between something happening in a program due to either a Math.Random (seed PRNG) and something happening every nth time.

So, picture you have a queue of items, every 10th item will be stamped.

This is linear/static probability. It will occur every time, on the 10th time.

Now, if I utilize Math.Random, and set the check to 10% (Math.Random()*100 < 10) then the probability is no longer static. It is dynamic, and while Mathematically I would like to say out of 100 times you would think probability would state that both will have fired 10 times. This is obviously not going to be the case in a real test, at run-time.

So I'm asking the community here, how would you explain this concept to a lamen. Am I getting something wrong here?

What would be the best way to visualize, or graph the outcomes of each? Comparison of the 1 out of 10th vs 10% is what I'm looking for, to say they are functionally the same is to miss the nuance involved, so I'm trying to showcase this.

Answer 1

First of all, you seem a bit confused with the terms linear, static and dynamic probability. Your first probability stays the same every time, so it is "constant".

In the second case, it is "not constant", i.e. it is variable. You may call it dynamic but I don't think this is common term. Now, when if a variable is linear, it changes by a constant value every time (mathematically following the formula a*x+b).

For example, the first time your prob. is 5*1+3=8%, the second time it is 5*2+3=13%, the third time 5*3+3=18%, the fourth 5*4+3=23%, etc.

In your second case, you don't have linear probability. I don't know which term would be appropriate; perhaps, just random probability (but constant and with the "programming" idea of randomness not the mathematical)

The second thing you need to consider is that when mathematicians define probability they imply that something is observed/happening over the long run or, as they like to say, on average.

For example, what is the probability for the engine of an aeroplane to fail? This is the same as asking how often do air jet engines fail over engine's life time? Say, for example it is 0.5%. This means that if an engine works for 180,000 hours (the long run in this case) the engine will fail 900 times.

Now, an example from programming (which apparently is not the best one). Think of a server which accepts requests from a browser to show a web page. The server is up for the next year, 24hrs a day.

If the server fails every 10th day, it means it is down 10th Jan, 20th Jan, 30th Jan, 9th Feb, 19th feb, 29th Feb/01 Mar and so on.

If the server probability for the server to fail is 10%, this means that out of the 365 days in a year, 36.5 days the server is down. This may happen in many different ways.

For example, the server can be down all January and 5.5 days in February. Or, 10 days in January, 10 days in March and 16.5 in August Or, 35 days in November, and 11.5 days in December Or, 3 days every month Or, ...

You can interpret the figure in hours instead of days but the logic is the same.

In both cases, the server is down 10% of the time or the probability of the server to be down is 10% or the server is down on average 10% of the time.