Probability Over 2 Sequences Of Trials

#1
Hey everyone!

I'm coding a program that identifies appearances of a lowercase "x" in a base64 encoded string. Like the following:

DWADCrxV+PhR4zxkQrIMUtarkN11aitHI8DEnzyG19CD...

I know the probability of finding at least one "x" in a sequence of 10 chars.
My doubt is about dealing with multiple sequences of 10 chars. I mean, as I see, they can be overlapping or non-overlapping:

[NON-OVERLAPPING]
DWADCrxV+P hR4zxkQrIM ...

[OVERLAPPING]
DWADCrxV+P WADCrxV+Ph ...

To evaluate the probabilities of multiple sequences (being each sequence a trial), per example with the Binomial Distribution (and possibly doing a standardization to the Normal Distribution), how should I deal with the sequences? Going for the overlapping approach or the non-overlapping? Knowing the probability of "x" appearing in one sequence, for two is valid to do p²?

Thanks in advance!