2. [Independence] You roll a fair die twice: all 36 outcomes are equally likely. Let be the event that the rst roll is 1, 2, or 3. Le? be the event that the second roll is 6. Finally, let C be the event that the sum of the rolls is even. (a) (3 pts) Show thatA J] B, A J'- C, andB J'- C (events are pairwise independent.) (b) (2 pts) Show thatAjLCSIB (A and C are not conditionally independent givenB.) 3. [Bernoulli Trials] You toss a coin independently 6 times. The coin is biased, the probability of a given toss being heads is}? Let's find out if it is more likely that none of them are heads or that half of them are heads. (a) (2 pts) What is the probability that you get no heads? (b) (2 pts) What is the probability that half of them are heads