I have 4 variables and I know the following probabilities:
1) $P(A|B_1)$; $P(A|B_2)$; $P(A|B_3)$;
2) $P(B_1)$; $P(B_2)$; $P(B_3)$.
Of course, I have:
4) $P(A,B_1)$; $P(A,B_2)$; $P(A,B_3)$;
And I need:
Is it possible calculate this probability using some rule o theorem of probability?
I was thinking to use Chain's rule but for this case, It is enough data.