1. Prove that <math>P(ABC) = P(B)P(C|B)P(A|BC)</math>:
Answer: <math>P(ABC) = P(A|BC)P(BC) = P(A|BC)P(C|B)P(B)</math>
2. What is the probability that the sum of two dice is odd with neither being a 4?
Answer: by enumerating all possibilities, the probability = 12/36 = 1/3