In a single throw of two dice, find the probability of
(i) getting a sum less than 6
(ii) getting a doublet of odd numbers
(iii) getting the sum as a prime number
(i) We know that,
Probability of occurrence of an event 
Outcomes are (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 no.of outcomes are 36
In that only (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1) are our desired outputs as there sum is less than 6
Therefore no.of desired outcomes are 10
Therefore, the probability of getting a sum less than 6
Conclusion: Probability of getting a sum less than 6, when two dice are rolled is 
(ii) We know that,
Probability of occurrence of an event 
In (a, b) if a=b then it is called a doublet
Total doublets are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
In (a, b) if a=b and if a, b both are odd then it is called a doublet
Odd doublets are (1, 1), (3, 3), (5, 5)
Outcomes are (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 no.of outcomes are 36 and desired outcomes are 3
Therefore, probability of getting doublet of odd numbers 
Conclusion: Probability of getting doublet of odd numbers, when two dice are rolled is 
(iii) We know that,
Probability of occurrence of an event 
Outcomes are (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 no.of outcomes are 36
Desired outputs are (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 no.of desired outputs are 15
Therefore, probability of getting the sum as a prime number 
Conclusion: Probability of getting the sum as a prime number, when two dice are rolled is 