Question

Write sample space ‘S’ and number of sample point n(S) for the following experiment. Also write events A, B, C in the set form and write n(A), n(B), n(C).

Two dice are rolled simultaneously,
Event  A : The sum of the digits on upper faces is a multiple of 6. 
Event B : The sum of the digits on the upper faces is minimum 10.
Event  C : The same digit on both the upper faces.

Answer 1

Two dice are rolled simultaneously.

Sample Space (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) Event  A : The sum of the digits on upper faces is a multiple of 6. 

A = {(1, 5) (2, 4) (3, 3) (4, 2) (5, 1) (6, 6)}

∴ n(A) = 6

(ii) Event B : The sum of the digits on the upper faces is minimum 10.

B = {(4, 6) (5, 5) (5, 6) (6, 4) (6, 5) (6, 6)}
∴ n(B) = 6

(iii) Event  C : The same digit on both the upper faces.

C = {(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)}
∴ n(C) = 6