1. [4 points) suppose you have a bag of 12 four sided dices. let the four sides be s1, s2, s3, and s4. eight of these 12 dices are fair, that is, sides of these eight dices have labels 1, 2, 3, and 4 on sides s1, s2, s3, and s4, respectively. but four dices are unfair, that is, sides of these four dices have labels 1, 1, 2, and 2 on sides s1, s2, s3, and s4, respectively. if a fair dice is tossed, probability of getting 1 = probability of getting 2 = probability of getting 3 = probability of getting 4 = 1/4. if an unfair dice is tossed, probability of getting 1 = probability of getting 2 = 1/2 and probability of getting 3 = probability of getting 4 = 0. let x = x1 + x2 + + x12 be a random variable denoting the total number ‘l's when all 12 dices are tossed togehter. (a) how many possible values x can take? for example, if one tosses two dices, the number of total 'l's could be 0, 1, 2. (b) how many ways the value of x could be 1? (c) how many ways the value of x could be 2? (d) how many ways the value of x could be 5? () use indicator random variables to compute expected number of 'l's, if all 12 dices are tossed together.