Probability of occurrence of an event = (Total number of favorable outcomes) / (Total number of outcomes)
Possible outcomes are as follow:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (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), (6, 5), (6, 6)
Total number of outcomes = 36
(i) getting a sum less than 6
Pick entries having sum less than 6:
(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)
Total number of favorable outcomes = 10
Probability (getting a sum less than 6) = 10/36 or 5/18
(ii) getting a doublet of odd numbers
Pick entries having doublet of odd numbers:
(1, 1), (3, 3), (5, 5)
Total number of favorable outcomes = 3
Probability (getting a doublet of odd numbers) = 3/36 or 1/12
(iii) getting the sum as a prime number
Pick entries having sum as a prime number:
(1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5)
Total number of favorable outcomes = 15
Probability (getting the sum as a prime number) = 15/36 or 5/12
