$\def\P{\operatorname{\sf P}}$I have universe with a population where people have one of 3 health problem($H_i$). There are 3 symptoms and each person can have from 0 to 3 symptoms, that are independent of each others.
I have the values of $\P(H_i)$, $\P(S_j)$, $\P(S_j\mid H_i)$, for every $i,j$ possible combinations.
From that I get the values of $\P(\overline S_j\mid H_i)=1-\P(S_j\mid H_i)$, for every $i,j$ possible combinations.
After that, I get the values for $\P(H_i\mid S_j)$ and $\P(H_i|\overline S_j)$ using Bayes Theorem, also for every i,j possible combinations..
I need to get the value of $\P(H_1\mid S_1\cap S_2)$, where $S_1$ and $S_2$ are independent.
Can anyone help me?