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

Number of outcomes with even sum \(\displaystyle =18\)

\(\displaystyle (1,1)(1,3)(1,5)(3,1)(3,3)(3,5)(5,1)(5,3)(5,5),(2,2)(2,4)(2,6) (4,2)(4,4)(4,6)(6,2)(6,4)(6,6)\)

\(\displaystyle \mathrm{P}(\) even sum \(\displaystyle )=\frac{18}{36}\) or \(\displaystyle \frac{1}{2}\)

Number of outcomes with even product = $\displaystyle 27$

\(\displaystyle (1,2)(1,4)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,2)(3,4)(3,6)\) $\displaystyle (4,1)$ \(\displaystyle (4,2)(4,3)(4,4)(4,5)(4,6)(5,2)(5,4)(5,6)(6,1)(6,2)(6,3) (6,4)(6,5)(6,6)\)

\(\displaystyle \mathrm{P}(\) even product \(\displaystyle )=\frac{27}{36}\) or \(\displaystyle \frac{3}{4}\)