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Math Help - Calculating probabilities in parallel recurring sequences

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    Calculating probabilities in parallel recurring sequences

    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?
    Last edited by Hwarazmi; April 13th 2013 at 04:49 AM.
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