Answer the following questions: A. Using only the definition of conditional probability, prove that P(a | a ^ b) = 1. [5pts] B. Show that the following statements are equivalent: (1) P(a | b) = P(a) (2) P(b | a) = P(b) (3) P(a ^\ b) = P(a)P(b) That is, any two of these statements are equivalent. [15pts]