# How do I find the frequency or percentage chance for two independent timed events to happen simultaneously?

If I have two events that occur on a specific interval (one every 8 seconds, the other every 200 milliseconds) but were not started synchronously, how can I calculate the frequency with which these two events will occur at the same time?

Looking at the numbers, it seems that unless they start synchronously, they will never coincide. If they started synchronously, in a perfect world, it would be every 8 seconds.

Obviously there is some variation/imperfection because they do coincide occasionally despite not starting at the same time.

I suppose I am looking for a harmonic, or additive function. Forgive me, my math knowledge is lacking.

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They need not start synchronously. For example, if event $E_{200ms}$ starts at a multiple of 200ms (200ms, 400ms, 600ms and so on) after event $E_{8s}$ has occurred then they will coincide. –  jay-sun Jan 3 '13 at 17:44
True; I should amend that to say if E_200ms doesn't start on a common denominator. (Grr, I give up on TEX formatting...) –  JYelton Jan 3 '13 at 17:51
Just a comment: if each event happens $\mathit{exactly}$ every $k$'th second, there is no probability involved - the process is purely deterministic –  Alex Jan 3 '13 at 23:14
They should be exact, but there is some variation, the amount of which is difficult to measure and not really that important. So, treating these as if they are on exact frequencies, what is a better way to tag the question since probability is not really applicable? –  JYelton Jan 3 '13 at 23:27

So if $E_{8s}$ starts at 0ms, and $E_{200ms}$ starts at 50ms, the LCM is 8000*50 ms or 40 seconds? –  JYelton Jan 3 '13 at 18:03