Sticker wrote: > I have a question, how to calculate the probability as following: > P(A1 & A2 & A3 | B)? > Given the condition that event B happens, how to calculate the > probability of all A1, A2 and A3 happen? Here A1, A2, A3 are > independent with each other but they are dependent with B separately. > > Can I say: > > P(A1 & A2 & A3 | B) = P(A1 | B) * P(A2 | B) * P(A3 | B)?
In general, no. Marginal independence does not imply conditional independence. Look up "Simpson's paradox".