In a simultaneous thrown of a pair of dice, find the probability of getting:
(i) 8 as the sum  
(ii)  a doublet
(iii) a doublet of prime number    
(iv) a doublet of odd number

Explanation

When a pair of dice is thrown simultaneously total number of outcome is `6 xx 6=36`.
(i) To get `8` as a sum outcomes are`(2,6),(6,2),(3,5),(5,3),(4,4)`
Total number of outcome is `5`
Therefore, the probability of getting `8` as sum is `=5/36`

(ii)To get doublet the outcomes are`(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)`
Total number of outcome is `6`.
Therefore, probability of getting doublet is `6/36=1/6`.

(iii)To get the doublet of prime number the outcomes are `(2,2),(3,3),(5,5)`
Total number of outcome is 3.
Therefore probability of getting doublet of prime number is `3/36=1/12`.

(iv) To get doublet of odd number the outcomes are `(1,1), (3,3),(5,5)`.
Total number of outcomes is `3` .
Therefore probability of getting doublet of odd numbers is `3/36=1/12`.