I have an unknown string S of length n. I have to given small string A1 and A2. Supposed that I know the probability of S.contains(A1) = true (which mean A1 appears in S at least once) and S.contains (A2) = true.
How do we compute the probability of S.contains(A1) && S.contains(A2)?
The general problem: Compute the probability P[S.contains(A1) && S.contains(A2) && ... && S.contains(An)] when we know P[S.contains(A1)], P[S.contains(A2)], ..., P[S.contains(An)]
Thank you
Update: We can compute P[S.contains(x) == true] in which x is an arbitrary string.
I guess if intersection of A1 and A2 is 0, then you should simply multiply the Pr(A1) and Pr(A2). or if you know probability of S.contains(A1) or S.contains(A2) you can simply subtract it from P(S.contains(A1) + p(S.contains(A2))