Sample Space for total number of possible outcomes are (1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(21),(2,2),(2,3),(2,4),(2,5), (2,6),(3,1),(3,2)(3,3), (3,4), (3,5), (3,6),(4,1),(4,2), (4,3)(4,4), (4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6), (6,1), (6,2), (6,3), (6,4),(65),(6,6) Total number of outcomes = 36 (i) Favorable outcomes =15

. Hence the probability of getting the sum as a prime number = 15/36 = 5/2 . (ii) Favorable outcomes for sum as prime total of atleast 10 are (4,6),(5,5),(5,6),(6,4),(6,5),(6,6), Number of favorable outcomes = 6 . Hence , the probability of getting a total of atleast 10 = 6/36 = 1=6 . (iii) Favorable outcomes for a doublet of even number are (2,2),(4,4),(6,6), Number of favorable outcomes = 3 . Hence, the probability of getting a doubt of even number = 3/36 = 1/36 = 1/13 . (iv) Favorable outcomes for a multiple of 2 on one dice and a multiple of 3 on the other dice are (2,3),(2,6),(3,2),(3,4),(3,6),(4,3),(4,6),(6,2) Number of favorable outcomes = 11 . Hence, the probability of getting a multiple of 2 on one dice and a multiple of 03 on the other dice = 11/36 . (v) Favorable outcomes for getting a multiple of 3 as a sum (1,2),(1,5),(2,1),(2,4),(3,3),(3,6),(4,2),(4,5), Number of favorable outcome to = 12 . Hence, the probability of getting a multiple of 3 as the sum = 12/36 = 1/3 . Q.2 Two identical but identifiable dice are tossed simultaneously . Find the probability associated with all possible total scores (2 through 12)