Suppose that three events A, B and C affect each other in the following way.?

P(B|C)=1/2


P(B|C')=1/3


P(A|B)=1/2


P(A|B')=1/3


Further assume that:


P(A|B n C) = P(A|B), and


P(A|B' n C) = P(A|B').


Calculate P(A|C) and P(A|C').





P represents the probability of an event and n represents the intersection of two events.

Suppose that three events A, B and C affect each other in the following way.?
P(A|B∩C) = P(A ∩ (B∩C)) / P(B∩C)





= P(A)P(B∩C)/P(B∩C)





= P(A)P(B)P(C)/P(B)P(C) = P(A|B)P(C)/P(C) = P(A|B) = ½





P(A|C) = P(A∩C)/P(C) = P(A)P(C)P(B)/P(B)P(C)





= P(A|B)P(B)P(C) / P(B∩C)





= P(A|B) P(B∩C) / P(B∩C)





= P(A|B) = ½





and similarly P(A|C') = 1/3