Two dice are thrown simultaneously . Find the probability of getting
(i) an even number as the sum.
(ii) a total of at least 10
(iii) a doublet of even number .

Explanation

`S={{:("(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)"):}}`
n(S) = 36
(i) Probability of even number as the sum ` = (cancel(18))/(underset(2)cancel(36)) =(1)/(2)`
(ii) Probability of total of at least 10 ` (cancel(6))/(underset(6)cancel(36))=(1)/(6)`
(iii) Probability of a doublet of even numbers `=(cancel(9))/(underset(4)cancel(36)) = (1)/(4)`