Let's say that I have a population that I can split into two subgroups, containing $60 \% $ and $40 \% $ of the population respectively.
And I know the probability of some event in each of the two groups:
$P_1(A|B) = p_1$
$P_2(A|B) = p_2$
I want to calculate the probability of the event in the entire population. Can we simply assume that it will be:
$P(A|B) = 0.6p_1 + 0.4p_2$