$P(O|v) = P(v|O)P(O) + P(v|O^c)P(O^c)$.
Is that true where v is a vector? If it is, how? I faced something similar in some article, it said it is driven by Bayes rule but I do not see how. (This is simplfied version if that is false I will consider the meaning of the terms to understand that.) Element in vector v are independent.