Suppose AAA and BBB are events with P(A∣B)=P(A∣Bc)=k.P(A|B) = P(A|B^c) = k.P(A∣B)=P(A∣Bc)=k. Which of the following must be true?
P(A)=kP(A) = kP(A)=k
P(B)=kP(B) = kP(B)=k
P(A∣B)=P(B∣A)P(A|B) = P(B|A)P(A∣B)=P(B∣A)
AAA and BBB are disjoint