Two dice are rolled. Write the sample space ‘S’ and number of sample points \(n(S)\). Also write the events in the set form and number of sample points in the event according to the given condition.(a) Condition for event A : Sum of the digits on upp…

Answer: \(n(S) = 36\); A = {(1,4), (2,3), (3,2), (4,1), (4,6), (5,5), (6,4)}, \(n(A) = 7\); B = { }, \(n(B) = 0\).

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)}, so \(n(S) = 36\).

(a) Sum a multiple of 5 means sum 5 or 10 :
A = {(1,4), (2,3), (3,2), (4,1), (4,6), (5,5), (6,4)}, \(n(A) = 7\).

(b) The maximum sum on two dice is 12, so a sum of 25 is impossible : B = { } (null set), \(n(B) = 0\).