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

Let for instance
$$\langle g_i\rangle  :=\{1,1,1,6,1,1,1,6,...,1,1,1,6\}$$ and
$$\langle h_i\rangle  :=\{1,1,1,1,6,1,1,1,1,6,...,1,1,1,1,6\}$$

be to recurrent chains of identical length $i_{\max}=20$

How can one calculate the probability that at a certain selected index $i_*$ we would have on both chains a $1$, i.o.w.:

$$\langle g_{i_*}\rangle =\langle h_{i_*}\rangle =1$$

to explain further the expansion of the problem...
let $\langle a_{i,m} \rangle$ be $m$ recurring sequences (in above example $m=\{1,2\}$) each with different frequencies of recurrence $f_m$ (above example $f_m=\{4,5\}$) and the identical entrained length of $L=\prod_{m}f_m$.
How can I calculate the probability that (only) the 1s (the digits 1) of all $m$ chains would be compatible?