Calculating probabilities in parallel recurring sequences

I am working with certain recurring sequences in genetics and try to calculate certain probabilities:

Let for instance

and

be to recurrent chains of identical length

How can one calculate the probability that at a certain selected index we would have on both chains a , i.o.w.:

to explain further the expansion of the problem...

let be recurring sequences (in above example ) each with different frequencies of recurrence (above example ) and the identical entrained length of .

How can I calculate the probability that (only) the 1s (the digits 1) of all chains would be compatible?