Suppose P(A∣B)=P(A∣Bc)P(A|B) = P(A|B^c)P(A∣B)=P(A∣Bc). What does this imply about events AAA and BBB?
AAA and BBB are disjoint
AAA and BBB are independent
P(A)=1P(A) = 1P(A)=1
AAA and BBB must be identical