Two fair dice are thrown, find the probability of the following events that the sum of the scores on their upper faces is (a) less than four (b) Multiple of 5 (c) Perfect square

 Since Two dice are thrown, ∴ The Sample Space  = {(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 (a) Let A = Event of getting the sum of the scores on the upper faces of dice is less than 4 ∴ A = {(1 , 1) (1 , 2) (2 , 1)) ∴ n(A) = 3 ∴ P(A) =n(A) / n(S) ∴ P(A) = 3 / 36 ∴ P(A) = 1 / 12 (b) Let B = Event of getting the sum of the scores on the upper faces of dice is multiple of 5. ∴ B = { ( 1 , 4) ( 2 , 3) (3 , 2) ( 4 , 1) (4 , 6) ( 5 , 5) ( 6 , 4 ) } ∴ n(B)  = 7 ∴ P(B) = n(B) / n(S) ∴ P(B) = 7/36 (c) Let C =  Event of getting the sum of the scores on the upper faces of dice is a perfect square. C = {(1 , 3) (2 , 2) (3 , 1) (3 , 6) (4 , 5) ( 5 , 4) ( 6 , 3) } ∴ n(C) = 7 ∴ P(C ) = n(C) / n(S) ∴ P(C) = 7 / 36