Two different dice are thrown together. Find the probability that the numbers obtained have (i) even sum, and (ii) even product.

When two different dice are thrown together, the sample space is given by
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
A = event that sum of nos is even.
A = { (1,1)(1,3)(1,5)(2,2)(2,4)(2,6)(3,1)(3,3)(3,5)(4,2)(4,4)(4,6)(5,1)(5,3)(5,5)(6,2)(6,4)(6,6) }
n(A) = 18
P(A) = \frac{n(A)}{n(S)} = \frac{18}{36} = \frac{1}{2}
B = event that the product is even.
B = { (1,2)(1,4)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,2)(3,4)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,2)(5,4)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6) }
n(B) = 27
P(B) = \frac{n(B)}{n(S)} = \frac{27}{36} = \frac{3}{4}