Hannah is hosting a halloween party for the cis 160 tas and has designed a game. the game consists of one player rolling a fair six-sided die twice; the player then wins s pieces of candy where s is the sum of the two rolls. for example, if the player rolls a 2 and then a 3, they will win 5 pieces of candy. note that each of the 36 possible outcomes of the two rolls is equally likely and has probability 1/36. as a cis 160 ta, hannah comes up with several conjectures about the game and has asked you answer them. (a) let aj be the event that the first roll is i and let b, be the event that the second roll results is j. are ai and b; independent? (b) let a be the event that the first roll is a 1 and b be the event that the sum of the two rolls is a 7. are a and b independent? (c) let a be the event that the maximum of the two rolls is 3 and b be the event that the minimum of the two rolls is 3. are a and b independent?