Question 1 (16 points) John rolls a pair of dice and gets two top numbers S, and $2. Let S = IS1 - Sal. Answer the following questions. (1) Determine the probability of getting S = 4 in a roll. [2K] (2) Determine the expectation of the variable S. [2K] (3) If he rolls the two dice repeatedly for 20 times, what is the probability that he rolls S = 4 exactly five times? [3K] (4) If he rolls the dice repeatedly, how many times should he reasonably expect to roll to have S = 4 five times? [3A] (5) If he rolls the two dice repeatedly, what is the probability that he didn't have S=4 for the first 6 trials? [3A] (6) Given S1x S2 = 12 in a particular roll, what is the probability S = 4? [3A]